LMFDB - Embedded newform 1232.2.q.n.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} - 2x^{5} + 66x^{4} - 9x^{3} + 136x^{2} + 15x + 225 $ x^8 + 9x^6 - 2x^5 + 66x^4 - 9x^3 + 136x^2 + 15x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.2
Root			$1.24132 - 2.15004i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.n.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08177 + 1.87368i) q^{3} +(1.74132 + 3.01606i) q^{5} +(-2.52609 + 0.786673i) q^{7} +(-0.840445 - 1.45569i) q^{9} +O(q^{10})$	\(q+(-1.08177 + 1.87368i) q^{3} +(1.74132 + 3.01606i) q^{5} +(-2.52609 + 0.786673i) q^{7} +(-0.840445 - 1.45569i) q^{9} +(-0.500000 + 0.866025i) q^{11} -2.16354 q^{13} -7.53483 q^{15} +(-1.03832 + 1.79843i) q^{17} +(-3.44432 - 5.96575i) q^{19} +(1.25868 - 5.58408i) q^{21} +(3.32309 + 5.75576i) q^{23} +(-3.56442 + 6.17375i) q^{25} -2.85394 q^{27} +1.84443 q^{29} +(0.862557 - 1.49399i) q^{31} +(-1.08177 - 1.87368i) q^{33} +(-6.77140 - 6.24900i) q^{35} +(-1.48265 - 2.56802i) q^{37} +(2.34044 - 4.05377i) q^{39} -1.55929 q^{41} +5.16354 q^{43} +(2.92697 - 5.06966i) q^{45} +(6.25404 + 10.8323i) q^{47} +(5.76229 - 3.97442i) q^{49} +(-2.24645 - 3.89096i) q^{51} +(3.18565 - 5.51770i) q^{53} -3.48265 q^{55} +14.9038 q^{57} +(-6.36654 + 11.0272i) q^{59} +(-6.91360 - 11.9747i) q^{61} +(3.26819 + 3.01606i) q^{63} +(-3.76742 - 6.52536i) q^{65} +(5.86141 - 10.1523i) q^{67} -14.3793 q^{69} -2.07664 q^{71} +(-6.95307 + 12.0431i) q^{73} +(-7.71174 - 13.3571i) q^{75} +(0.581768 - 2.58100i) q^{77} +(-1.88751 - 3.26926i) q^{79} +(5.60864 - 9.71445i) q^{81} +5.04194 q^{83} -7.23222 q^{85} +(-1.99524 + 3.45586i) q^{87} +(1.93920 + 3.35879i) q^{89} +(5.46529 - 1.70199i) q^{91} +(1.86617 + 3.23231i) q^{93} +(11.9954 - 20.7766i) q^{95} -3.94084 q^{97} +1.68089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.08177	+	1.87368i	−0.624559	+	1.08177i	0.364067	+	0.931373i	$0.381388\pi$
$3$	−1.08177	+	1.87368i	−0.624559	+	1.08177i	−0.988626	+	0.150395i	$0.951945\pi$
$4$		0			0
$5$	1.74132	+	3.01606i	0.778744	+	1.34882i	0.932666	+	0.360740i	$0.117476\pi$
$5$	1.74132	+	3.01606i	0.778744	+	1.34882i	−0.153923	+	0.988083i	$0.549191\pi$
$6$		0			0
$7$	−2.52609	+	0.786673i	−0.954773	+	0.297334i
$7$	−2.52609	+	0.786673i	−0.954773	+	0.297334i
$8$		0			0
$9$	−0.840445	−	1.45569i	−0.280148	−	0.485231i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−2.16354			−0.600057			−0.300029	−	0.953930i	$-0.596996\pi$
$13$	−2.16354			−0.600057			−0.300029	+	0.953930i	$0.596996\pi$
$14$		0			0
$15$	−7.53483			−1.94549
$16$		0			0
$17$	−1.03832	+	1.79843i	−0.251830	+	0.436183i	−0.964030	−	0.265794i	$-0.914366\pi$
$17$	−1.03832	+	1.79843i	−0.251830	+	0.436183i	0.712200	+	0.701977i	$0.247699\pi$
$18$		0			0
$19$	−3.44432	−	5.96575i	−0.790182	−	1.36864i	−0.925854	−	0.377882i	$-0.876652\pi$
$19$	−3.44432	−	5.96575i	−0.790182	−	1.36864i	0.135671	−	0.990754i	$-0.456681\pi$
$20$		0			0
$21$	1.25868	−	5.58408i	0.274666	−	1.21855i
$22$		0			0
$23$	3.32309	+	5.75576i	0.692913	+	1.20016i	0.970879	+	0.239569i	$0.0770061\pi$
$23$	3.32309	+	5.75576i	0.692913	+	1.20016i	−0.277967	+	0.960591i	$0.589661\pi$
$24$		0			0
$25$	−3.56442	+	6.17375i	−0.712883	+	1.23475i
$26$		0			0
$27$	−2.85394			−0.549242
$28$		0			0
$29$	1.84443			0.342501			0.171251	−	0.985228i	$-0.445219\pi$
$29$	1.84443			0.342501			0.171251	+	0.985228i	$0.445219\pi$
$30$		0			0
$31$	0.862557	−	1.49399i	0.154920	−	0.268329i	−0.778110	−	0.628128i	$-0.783821\pi$
$31$	0.862557	−	1.49399i	0.154920	−	0.268329i	0.933030	+	0.359799i	$0.117155\pi$
$32$		0			0
$33$	−1.08177	−	1.87368i	−0.188312	−	0.326165i
$34$		0			0
$35$	−6.77140	−	6.24900i	−1.14458	−	1.05627i
$36$		0			0
$37$	−1.48265	−	2.56802i	−0.243746	−	0.422180i	0.718033	−	0.696010i	$-0.245043\pi$
$37$	−1.48265	−	2.56802i	−0.243746	−	0.422180i	−0.961778	+	0.273830i	$0.911710\pi$
$38$		0			0
$39$	2.34044	−	4.05377i	0.374771	−	0.649123i
$40$		0			0
$41$	−1.55929			−0.243520			−0.121760	−	0.992560i	$-0.538854\pi$
$41$	−1.55929			−0.243520			−0.121760	+	0.992560i	$0.538854\pi$
$42$		0			0
$43$	5.16354			0.787432			0.393716	−	0.919232i	$-0.371189\pi$
$43$	5.16354			0.787432			0.393716	+	0.919232i	$0.371189\pi$
$44$		0			0
$45$	2.92697	−	5.06966i	0.436327	−	0.755741i
$46$		0			0
$47$	6.25404	+	10.8323i	0.912246	+	1.58006i	0.810884	+	0.585207i	$0.198987\pi$
$47$	6.25404	+	10.8323i	0.912246	+	1.58006i	0.101362	+	0.994850i	$0.467680\pi$
$48$		0			0
$49$	5.76229	−	3.97442i	0.823185	−	0.567774i
$50$		0			0
$51$	−2.24645	−	3.89096i	−0.314566	−	0.544844i
$52$		0			0
$53$	3.18565	−	5.51770i	0.437582	−	0.757915i	−0.559920	−	0.828547i	$-0.689168\pi$
$53$	3.18565	−	5.51770i	0.437582	−	0.757915i	0.997502	+	0.0706316i	$0.0225015\pi$
$54$		0			0
$55$	−3.48265			−0.469600
$56$		0			0
$57$	14.9038			1.97406
$58$		0			0
$59$	−6.36654	+	11.0272i	−0.828853	+	1.43561i	0.0700863	+	0.997541i	$0.477673\pi$
$59$	−6.36654	+	11.0272i	−0.828853	+	1.43561i	−0.898939	+	0.438074i	$0.855661\pi$
$60$		0			0
$61$	−6.91360	−	11.9747i	−0.885196	−	1.53320i	−0.845489	−	0.533993i	$-0.820691\pi$
$61$	−6.91360	−	11.9747i	−0.885196	−	1.53320i	−0.0397066	−	0.999211i	$-0.512642\pi$
$62$		0			0
$63$	3.26819	+	3.01606i	0.411754	+	0.379988i
$64$		0			0
$65$	−3.76742	−	6.52536i	−0.467291	−	0.809371i
$66$		0			0
$67$	5.86141	−	10.1523i	0.716086	−	1.24030i	−0.246454	−	0.969155i	$-0.579265\pi$
$67$	5.86141	−	10.1523i	0.716086	−	1.24030i	0.962539	−	0.271142i	$-0.0874014\pi$
$68$		0			0
$69$	−14.3793			−1.73106
$70$		0			0
$71$	−2.07664			−0.246452			−0.123226	−	0.992379i	$-0.539324\pi$
$71$	−2.07664			−0.246452			−0.123226	+	0.992379i	$0.539324\pi$
$72$		0			0
$73$	−6.95307	+	12.0431i	−0.813795	+	1.40953i	0.0963954	+	0.995343i	$0.469269\pi$
$73$	−6.95307	+	12.0431i	−0.813795	+	1.40953i	−0.910190	+	0.414191i	$0.864065\pi$
$74$		0			0
$75$	−7.71174	−	13.3571i	−0.890475	−	1.54235i
$76$		0			0
$77$	0.581768	−	2.58100i	0.0662986	−	0.294132i
$78$		0			0
$79$	−1.88751	−	3.26926i	−0.212361	−	0.367820i	0.740092	−	0.672506i	$-0.234782\pi$
$79$	−1.88751	−	3.26926i	−0.212361	−	0.367820i	−0.952453	+	0.304686i	$0.901449\pi$
$80$		0			0
$81$	5.60864	−	9.71445i	0.623182	−	1.07938i
$82$		0			0
$83$	5.04194			0.553425			0.276712	−	0.960953i	$-0.410755\pi$
$83$	5.04194			0.553425			0.276712	+	0.960953i	$0.410755\pi$
$84$		0			0
$85$	−7.23222			−0.784444
$86$		0			0
$87$	−1.99524	+	3.45586i	−0.213912	+	0.370507i
$88$		0			0
$89$	1.93920	+	3.35879i	0.205555	+	0.356032i	0.950309	−	0.311307i	$-0.100767\pi$
$89$	1.93920	+	3.35879i	0.205555	+	0.356032i	−0.744754	+	0.667339i	$0.767433\pi$
$90$		0			0
$91$	5.46529	−	1.70199i	0.572918	−	0.178418i
$92$		0			0
$93$	1.86617	+	3.23231i	0.193513	+	0.335175i
$94$		0			0
$95$	11.9954	−	20.7766i	1.23070	−	2.13163i
$96$		0			0
$97$	−3.94084			−0.400131			−0.200066	−	0.979782i	$-0.564116\pi$
$97$	−3.94084			−0.400131			−0.200066	+	0.979782i	$0.564116\pi$
$98$		0			0
$99$	1.68089			0.168936
$100$		0			0
$101$	−2.78875	+	4.83026i	−0.277491	+	0.480629i	−0.970761	−	0.240050i	$-0.922836\pi$
$101$	−2.78875	+	4.83026i	−0.277491	+	0.480629i	0.693270	+	0.720678i	$0.256170\pi$
$102$		0			0
$103$	−8.12485	−	14.0727i	−0.800565	−	1.38662i	−0.919245	−	0.393687i	$-0.871199\pi$
$103$	−8.12485	−	14.0727i	−0.800565	−	1.38662i	0.118679	−	0.992933i	$-0.462134\pi$
$104$		0			0
$105$	19.0337	−	5.92745i	1.85750	−	0.578460i
$106$		0			0
$107$	1.14733	+	1.98723i	0.110916	+	0.192113i	0.916140	−	0.400859i	$-0.131288\pi$
$107$	1.14733	+	1.98723i	0.110916	+	0.192113i	−0.805224	+	0.592971i	$0.797955\pi$
$108$		0			0
$109$	−5.71687	+	9.90190i	−0.547576	+	0.948430i	0.450863	+	0.892593i	$0.351116\pi$
$109$	−5.71687	+	9.90190i	−0.547576	+	0.948430i	−0.998440	+	0.0558372i	$0.982217\pi$
$110$		0			0
$111$	6.41552			0.608934
$112$		0			0
$113$	−7.42348			−0.698343			−0.349171	−	0.937059i	$-0.613537\pi$
$113$	−7.42348			−0.698343			−0.349171	+	0.937059i	$0.613537\pi$
$114$		0			0
$115$	−11.5732	+	20.0453i	−1.07920	+	1.86923i
$116$		0			0
$117$	1.81833	+	3.14944i	0.168105	+	0.291166i
$118$		0			0
$119$	1.20813	−	5.35981i	0.110749	−	0.491333i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	1.68679	−	2.92161i	0.152093	−	0.263433i
$124$		0			0
$125$	−7.41396			−0.663125
$126$		0			0
$127$	8.88636			0.788537			0.394269	−	0.918995i	$-0.370998\pi$
$127$	8.88636			0.788537			0.394269	+	0.918995i	$0.370998\pi$
$128$		0			0
$129$	−5.58575	+	9.67480i	−0.491798	+	0.851819i
$130$		0			0
$131$	−2.93920	−	5.09085i	−0.256799	−	0.444789i	0.708583	−	0.705627i	$-0.249335\pi$
$131$	−2.93920	−	5.09085i	−0.256799	−	0.444789i	−0.965383	+	0.260838i	$0.916001\pi$
$132$		0			0
$133$	13.3938	+	12.3605i	1.16139	+	1.07179i
$134$		0			0
$135$	−4.96964	−	8.60767i	−0.427718	−	0.740830i
$136$		0			0
$137$	−9.17626	+	15.8937i	−0.783981	+	1.35789i	0.145626	+	0.989340i	$0.453481\pi$
$137$	−9.17626	+	15.8937i	−0.783981	+	1.35789i	−0.929606	+	0.368554i	$0.879853\pi$
$138$		0			0
$139$	−21.7925			−1.84842			−0.924208	−	0.381890i	$-0.875273\pi$
$139$	−21.7925			−1.84842			−0.924208	+	0.381890i	$0.875273\pi$
$140$		0			0
$141$	−27.0617			−2.27901
$142$		0			0
$143$	1.08177	−	1.87368i	0.0904620	−	0.156685i
$144$		0			0
$145$	3.21174	+	5.56290i	0.266721	+	0.461974i
$146$		0			0
$147$	1.21331	+	15.0961i	0.100072	+	1.24510i
$148$		0			0
$149$	−5.17342	−	8.96063i	−0.423823	−	0.734083i	0.572487	−	0.819914i	$-0.305979\pi$
$149$	−5.17342	−	8.96063i	−0.423823	−	0.734083i	−0.996310	+	0.0858310i	$0.972645\pi$
$150$		0			0
$151$	−1.91823	+	3.32248i	−0.156103	+	0.270379i	−0.933460	−	0.358681i	$-0.883227\pi$
$151$	−1.91823	+	3.32248i	−0.156103	+	0.270379i	0.777357	+	0.629060i	$0.216560\pi$
$152$		0			0
$153$	3.49061			0.282199
$154$		0			0
$155$	6.00796			0.482571
$156$		0			0
$157$	2.39612	−	4.15020i	0.191231	−	0.331222i	−0.754427	−	0.656384i	$-0.772085\pi$
$157$	2.39612	−	4.15020i	0.191231	−	0.331222i	0.945659	+	0.325161i	$0.105419\pi$
$158$		0			0
$159$	6.89227	+	11.9378i	0.546592	+	0.946726i
$160$		0			0
$161$	−12.9223	−	11.9254i	−1.01842	−	0.939854i
$162$		0			0
$163$	3.94794	+	6.83803i	0.309227	+	0.535596i	0.978193	−	0.207696i	$-0.0665965\pi$
$163$	3.94794	+	6.83803i	0.309227	+	0.535596i	−0.668967	+	0.743292i	$0.733263\pi$
$164$		0			0
$165$	3.76742	−	6.52536i	0.293293	−	0.507998i
$166$		0			0
$167$	15.7955			1.22229			0.611147	−	0.791517i	$-0.290709\pi$
$167$	15.7955			1.22229			0.611147	+	0.791517i	$0.290709\pi$
$168$		0			0
$169$	−8.31911			−0.639932
$170$		0			0
$171$	−5.78953	+	10.0278i	−0.442736	+	0.766842i
$172$		0			0
$173$	0.952938	+	1.65054i	0.0724505	+	0.125488i	0.899975	−	0.435942i	$-0.143585\pi$
$173$	0.952938	+	1.65054i	0.0724505	+	0.125488i	−0.827524	+	0.561430i	$0.810251\pi$
$174$		0			0
$175$	4.14733	−	18.3995i	0.313508	−	1.39087i
$176$		0			0
$177$	−13.7742	−	23.8577i	−1.03533	−	1.79325i
$178$		0			0
$179$	−7.65890	+	13.2656i	−0.572453	+	0.991518i	0.423860	+	0.905728i	$0.360675\pi$
$179$	−7.65890	+	13.2656i	−0.572453	+	0.991518i	−0.996313	+	0.0857905i	$0.972658\pi$
$180$		0			0
$181$	21.5950			1.60514			0.802571	−	0.596556i	$-0.203465\pi$
$181$	21.5950			1.60514			0.802571	+	0.596556i	$0.203465\pi$
$182$		0			0
$183$	29.9156			2.21143
$184$		0			0
$185$	5.16354	−	8.94351i	0.379631	−	0.657540i
$186$		0			0
$187$	−1.03832	−	1.79843i	−0.0759296	−	0.131514i
$188$		0			0
$189$	7.20933	−	2.24512i	0.524401	−	0.163308i
$190$		0			0
$191$	−1.79187	−	3.10362i	−0.129655	−	0.224570i	0.793888	−	0.608065i	$-0.208054\pi$
$191$	−1.79187	−	3.10362i	−0.129655	−	0.224570i	−0.923543	+	0.383495i	$0.874720\pi$
$192$		0			0
$193$	−3.93522	+	6.81600i	−0.283263	+	0.490626i	−0.972187	−	0.234208i	$-0.924750\pi$
$193$	−3.93522	+	6.81600i	−0.283263	+	0.490626i	0.688923	+	0.724834i	$0.258084\pi$
$194$		0			0
$195$	16.3019			1.16740
$196$		0			0
$197$	−18.0419			−1.28543			−0.642717	−	0.766103i	$-0.722193\pi$
$197$	−18.0419			−1.28543			−0.642717	+	0.766103i	$0.722193\pi$
$198$		0			0
$199$	−13.0680	+	22.6345i	−0.926368	+	1.60452i	−0.137022	+	0.990568i	$0.543753\pi$
$199$	−13.0680	+	22.6345i	−0.926368	+	1.60452i	−0.789346	+	0.613949i	$0.789580\pi$
$200$		0			0
$201$	12.6814	+	21.9648i	0.894476	+	1.54928i
$202$		0			0
$203$	−4.65919	+	1.45096i	−0.327011	+	0.101837i
$204$		0			0
$205$	−2.71523	−	4.70292i	−0.189640	−	0.328466i
$206$		0			0
$207$	5.58575	−	9.67480i	0.388236	−	0.672445i
$208$		0			0
$209$	6.88865			0.476498
$210$		0			0
$211$	16.2577			1.11922			0.559612	−	0.828755i	$-0.310950\pi$
$211$	16.2577			1.11922			0.559612	+	0.828755i	$0.310950\pi$
$212$		0			0
$213$	2.24645	−	3.89096i	0.153924	−	0.266604i
$214$		0			0
$215$	8.99139	+	15.5735i	0.613208	+	1.06211i
$216$		0			0
$217$	−1.00362	+	4.45251i	−0.0681299	+	0.302256i
$218$		0			0
$219$	−15.0432	−	26.0556i	−1.01653	−	1.76067i
$220$		0			0
$221$	2.24645	−	3.89096i	0.151112	−	0.261734i
$222$		0			0
$223$	14.7228			0.985913			0.492957	−	0.870054i	$-0.335916\pi$
$223$	14.7228			0.985913			0.492957	+	0.870054i	$0.335916\pi$
$224$		0			0
$225$	11.9828			0.798852
$226$		0			0
$227$	−9.42221	+	16.3198i	−0.625374	+	1.08318i	0.363094	+	0.931752i	$0.381720\pi$
$227$	−9.42221	+	16.3198i	−0.625374	+	1.08318i	−0.988468	+	0.151427i	$0.951613\pi$
$228$		0			0
$229$	10.2580	+	17.7674i	0.677869	+	1.17410i	0.975621	+	0.219461i	$0.0704299\pi$
$229$	10.2580	+	17.7674i	0.677869	+	1.17410i	−0.297752	+	0.954643i	$0.596237\pi$
$230$		0			0
$231$	4.20662	+	3.88209i	0.276775	+	0.255423i
$232$		0			0
$233$	12.8276	+	22.2180i	0.840362	+	1.45555i	0.889589	+	0.456762i	$0.150991\pi$
$233$	12.8276	+	22.2180i	0.840362	+	1.45555i	−0.0492275	+	0.998788i	$0.515676\pi$
$234$		0			0
$235$	−21.7806	+	37.7252i	−1.42081	+	2.46092i
$236$		0			0
$237$	8.16738			0.530528
$238$		0			0
$239$	21.0879			1.36406			0.682031	−	0.731324i	$-0.261097\pi$
$239$	21.0879			1.36406			0.682031	+	0.731324i	$0.261097\pi$
$240$		0			0
$241$	−5.93558	+	10.2807i	−0.382345	+	0.662240i	−0.991397	−	0.130890i	$-0.958217\pi$
$241$	−5.93558	+	10.2807i	−0.382345	+	0.662240i	0.609052	+	0.793130i	$0.291550\pi$
$242$		0			0
$243$	7.85358	+	13.6028i	0.503807	+	0.872620i
$244$		0			0
$245$	22.0211	+	10.4587i	1.40688	+	0.668181i
$246$		0			0
$247$	7.45192	+	12.9071i	0.474154	+	0.821260i
$248$		0			0
$249$	−5.45421	+	9.44697i	−0.345646	+	0.598677i
$250$		0			0
$251$	−3.54280			−0.223619			−0.111810	−	0.993730i	$-0.535665\pi$
$251$	−3.54280			−0.223619			−0.111810	+	0.993730i	$0.535665\pi$
$252$		0			0
$253$	−6.64618			−0.417842
$254$		0			0
$255$	7.82358	−	13.5508i	0.489932	−	0.848587i
$256$		0			0
$257$	−6.34570	−	10.9911i	−0.395834	−	0.685604i	0.597374	−	0.801963i	$-0.296211\pi$
$257$	−6.34570	−	10.9911i	−0.395834	−	0.685604i	−0.993207	+	0.116359i	$0.962878\pi$
$258$		0			0
$259$	5.76550	+	5.32070i	0.358250	+	0.330612i
$260$		0			0
$261$	−1.55014	−	2.68492i	−0.0959511	−	0.166192i
$262$		0			0
$263$	−0.693897	+	1.20186i	−0.0427875	+	0.0741101i	−0.886626	−	0.462487i	$-0.846957\pi$
$263$	−0.693897	+	1.20186i	−0.0427875	+	0.0741101i	0.843839	+	0.536597i	$0.180291\pi$
$264$		0			0
$265$	22.1890			1.36306
$266$		0			0
$267$	−8.39106			−0.513525
$268$		0			0
$269$	−0.0260931	+	0.0451946i	−0.00159092	+	0.00275556i	−0.866820	−	0.498622i	$-0.833840\pi$
$269$	−0.0260931	+	0.0451946i	−0.00159092	+	0.00275556i	0.865229	+	0.501377i	$0.167173\pi$
$270$		0			0
$271$	−7.70776	−	13.3502i	−0.468213	−	0.810969i	0.531127	−	0.847292i	$-0.321769\pi$
$271$	−7.70776	−	13.3502i	−0.468213	−	0.810969i	−0.999340	+	0.0363233i	$0.988435\pi$
$272$		0			0
$273$	−2.72319	+	12.0814i	−0.164815	+	0.731197i
$274$		0			0
$275$	−3.56442	−	6.17375i	−0.214942	−	0.372291i
$276$		0			0
$277$	4.53804	−	7.86011i	0.272664	−	0.472268i	−0.696879	−	0.717189i	$-0.745429\pi$
$277$	4.53804	−	7.86011i	0.272664	−	0.472268i	0.969543	+	0.244921i	$0.0787619\pi$
$278$		0			0
$279$	−2.89972			−0.173602
$280$		0			0
$281$	14.2252			0.848607			0.424303	−	0.905520i	$-0.360519\pi$
$281$	14.2252			0.848607			0.424303	+	0.905520i	$0.360519\pi$
$282$		0			0
$283$	7.65016	−	13.2505i	0.454755	−	0.787659i	−0.543919	−	0.839138i	$-0.683060\pi$
$283$	7.65016	−	13.2505i	0.454755	−	0.787659i	0.998674	+	0.0514788i	$0.0163935\pi$
$284$		0			0
$285$	25.9524	+	44.9509i	1.53729	+	2.66266i
$286$		0			0
$287$	3.93891	−	1.22665i	0.232507	−	0.0724070i
$288$		0			0
$289$	6.34377	+	10.9877i	0.373163	+	0.646338i
$290$		0			0
$291$	4.26307	−	7.38386i	0.249906	−	0.432849i
$292$		0			0
$293$	−13.7086			−0.800866			−0.400433	−	0.916326i	$-0.631140\pi$
$293$	−13.7086			−0.800866			−0.400433	+	0.916326i	$0.631140\pi$
$294$		0			0
$295$	−44.3448			−2.58185
$296$		0			0
$297$	1.42697	−	2.47159i	0.0828013	−	0.143416i
$298$		0			0
$299$	−7.18963	−	12.4528i	−0.415787	−	0.720164i
$300$		0			0
$301$	−13.0436	+	4.06201i	−0.751819	+	0.234130i
$302$		0			0
$303$	−6.03356	−	10.4504i	−0.346619	−	0.600362i
$304$		0			0
$305$	24.0776	−	41.7037i	1.37868	−	2.38795i
$306$		0			0
$307$	−30.7215			−1.75337			−0.876685	−	0.481065i	$-0.840250\pi$
$307$	−30.7215			−1.75337			−0.876685	+	0.481065i	$0.840250\pi$
$308$		0			0
$309$	35.1568			2.00000
$310$		0			0
$311$	−5.09514	+	8.82504i	−0.288919	+	0.500422i	−0.973552	−	0.228466i	$-0.926629\pi$
$311$	−5.09514	+	8.82504i	−0.288919	+	0.500422i	0.684633	+	0.728888i	$0.259962\pi$
$312$		0			0
$313$	−4.98663	−	8.63709i	−0.281861	−	0.488197i	0.689982	−	0.723826i	$-0.257618\pi$
$313$	−4.98663	−	8.63709i	−0.281861	−	0.488197i	−0.971843	+	0.235629i	$0.924285\pi$
$314$		0			0
$315$	−3.40564	+	15.1090i	−0.191886	+	0.851296i
$316$		0			0
$317$	11.7975	+	20.4339i	0.662613	+	1.14768i	0.979927	+	0.199359i	$0.0638859\pi$
$317$	11.7975	+	20.4339i	0.662613	+	1.14768i	−0.317313	+	0.948321i	$0.602781\pi$
$318$		0			0
$319$	−0.922213	+	1.59732i	−0.0516340	+	0.0894327i
$320$		0			0
$321$	−4.96456			−0.277095
$322$		0			0
$323$	14.3053			0.795967
$324$		0			0
$325$	7.71174	−	13.3571i	0.427770	−	0.740920i
$326$		0			0
$327$	−12.3686	−	21.4231i	−0.683988	−	1.18470i
$328$		0			0
$329$	−24.3198	−	22.4436i	−1.34079	−	1.23735i
$330$		0			0
$331$	7.07750	+	12.2586i	0.389015	+	0.673793i	0.992317	−	0.123719i	$-0.0394822\pi$
$331$	7.07750	+	12.2586i	0.389015	+	0.673793i	−0.603303	+	0.797512i	$0.706149\pi$
$332$		0			0
$333$	−2.49217	+	4.31656i	−0.136570	+	0.236546i
$334$		0			0
$335$	40.8265			2.23059
$336$		0			0
$337$	10.4922			0.571545			0.285772	−	0.958298i	$-0.407750\pi$
$337$	10.4922			0.571545			0.285772	+	0.958298i	$0.407750\pi$
$338$		0			0
$339$	8.03049	−	13.9092i	0.436156	−	0.755445i
$340$		0			0
$341$	0.862557	+	1.49399i	0.0467101	+	0.0809042i
$342$		0			0
$343$	−11.4295	+	14.5728i	−0.617136	+	0.786856i
$344$		0			0
$345$	−25.0389	−	43.3687i	−1.34805	−	2.33489i
$346$		0			0
$347$	−13.2151	+	22.8892i	−0.709422	+	1.22876i	0.255650	+	0.966770i	$0.417711\pi$
$347$	−13.2151	+	22.8892i	−0.709422	+	1.22876i	−0.965072	+	0.261986i	$0.915623\pi$
$348$		0			0
$349$	25.7231			1.37693			0.688463	−	0.725272i	$-0.258286\pi$
$349$	25.7231			1.37693			0.688463	+	0.725272i	$0.258286\pi$
$350$		0			0
$351$	6.17461			0.329576
$352$		0			0
$353$	−3.52922	+	6.11278i	−0.187841	+	0.325351i	−0.944530	−	0.328424i	$-0.893482\pi$
$353$	−3.52922	+	6.11278i	−0.187841	+	0.325351i	0.756689	+	0.653775i	$0.226816\pi$
$354$		0			0
$355$	−3.61611	−	6.26329i	−0.191923	−	0.332421i
$356$		0			0
$357$	8.73565	+	8.06171i	0.462340	+	0.426671i
$358$		0			0
$359$	−6.85743	−	11.8774i	−0.361921	−	0.626866i	0.626356	−	0.779537i	$-0.284546\pi$
$359$	−6.85743	−	11.8774i	−0.361921	−	0.626866i	−0.988277	+	0.152671i	$0.951212\pi$
$360$		0			0
$361$	−14.2267	+	24.6415i	−0.748776	+	1.29692i
$362$		0			0
$363$	2.16354			0.113556
$364$		0			0
$365$	−48.4301			−2.53495
$366$		0			0
$367$	−14.0538	+	24.3419i	−0.733604	+	1.27064i	0.221730	+	0.975108i	$0.428830\pi$
$367$	−14.0538	+	24.3419i	−0.733604	+	1.27064i	−0.955333	+	0.295530i	$0.904504\pi$
$368$		0			0
$369$	1.31050	+	2.26985i	0.0682218	+	0.118164i
$370$		0			0
$371$	−3.70662	+	16.4443i	−0.192438	+	0.853745i
$372$		0			0
$373$	−8.89575	−	15.4079i	−0.460605	−	0.797791i	0.538386	−	0.842698i	$-0.319034\pi$
$373$	−8.89575	−	15.4079i	−0.460605	−	0.797791i	−0.998991	+	0.0449073i	$0.985701\pi$
$374$		0			0
$375$	8.02019	−	13.8914i	0.414161	−	0.717348i
$376$		0			0
$377$	−3.99048			−0.205520
$378$		0			0
$379$	−5.31911			−0.273224			−0.136612	−	0.990625i	$-0.543621\pi$
$379$	−5.31911			−0.273224			−0.136612	+	0.990625i	$0.543621\pi$
$380$		0			0
$381$	−9.61299	+	16.6502i	−0.492488	+	0.853015i
$382$		0			0
$383$	6.94318	+	12.0259i	0.354780	+	0.614497i	0.987080	−	0.160226i	$-0.0512224\pi$
$383$	6.94318	+	12.0259i	0.354780	+	0.614497i	−0.632300	+	0.774723i	$0.717889\pi$
$384$		0			0
$385$	8.79749	−	2.73970i	0.448362	−	0.139628i
$386$		0			0
$387$	−4.33967	−	7.51652i	−0.220598	−	0.382086i
$388$		0			0
$389$	2.57742	−	4.46423i	0.130681	−	0.226345i	−0.793259	−	0.608885i	$-0.791617\pi$
$389$	2.57742	−	4.46423i	0.130681	−	0.226345i	0.923939	+	0.382540i	$0.124950\pi$
$390$		0			0
$391$	−13.8018			−0.697985
$392$		0			0
$393$	12.7181			0.641545
$394$		0			0
$395$	6.57352	−	11.3857i	0.330750	−	0.572875i
$396$		0			0
$397$	5.05219	+	8.75064i	0.253562	+	0.439182i	0.964504	−	0.264068i	$-0.0850645\pi$
$397$	5.05219	+	8.75064i	0.253562	+	0.439182i	−0.710942	+	0.703251i	$0.751731\pi$
$398$		0			0
$399$	−37.6485	+	11.7244i	−1.88478	+	0.586956i
$400$		0			0
$401$	−17.1068	−	29.6299i	−0.854275	−	1.47965i	−0.877316	−	0.479913i	$-0.840668\pi$
$401$	−17.1068	−	29.6299i	−0.854275	−	1.47965i	0.0230408	−	0.999735i	$-0.492665\pi$
$402$		0			0
$403$	−1.86617	+	3.23231i	−0.0929607	+	0.161013i
$404$		0			0
$405$	39.0658			1.94120
$406$		0			0
$407$	2.96529			0.146984
$408$		0			0
$409$	−17.0783	+	29.5804i	−0.844467	+	1.46266i	0.0416171	+	0.999134i	$0.486749\pi$
$409$	−17.0783	+	29.5804i	−0.844467	+	1.46266i	−0.886084	+	0.463525i	$0.846584\pi$
$410$		0			0
$411$	−19.8532	−	34.3867i	−0.979284	−	1.69617i
$412$		0			0
$413$	7.40770	−	32.8640i	0.364509	−	1.61713i
$414$		0			0
$415$	8.77965	+	15.2068i	0.430976	+	0.746472i
$416$		0			0
$417$	23.5744	−	40.8321i	1.15444	−	1.99956i
$418$		0			0
$419$	−5.94724			−0.290542			−0.145271	−	0.989392i	$-0.546405\pi$
$419$	−5.94724			−0.290542			−0.145271	+	0.989392i	$0.546405\pi$
$420$		0			0
$421$	−5.21645			−0.254234			−0.127117	−	0.991888i	$-0.540572\pi$
$421$	−5.21645			−0.254234			−0.127117	+	0.991888i	$0.540572\pi$
$422$		0			0
$423$	10.5124	−	18.2079i	0.511128	−	0.885300i
$424$		0			0
$425$	−7.40202	−	12.8207i	−0.359051	−	0.621894i
$426$		0			0
$427$	26.8846	+	24.8105i	1.30104	+	1.20066i
$428$		0			0
$429$	2.34044	+	4.05377i	0.112998	+	0.195718i
$430$		0			0
$431$	10.7679	−	18.6506i	0.518672	−	0.898366i	−0.481093	−	0.876670i	$-0.659760\pi$
$431$	10.7679	−	18.6506i	0.518672	−	0.898366i	0.999765	−	0.0216964i	$-0.00690671\pi$
$432$		0			0
$433$	4.15786			0.199814			0.0999070	−	0.994997i	$-0.468145\pi$
$433$	4.15786			0.199814			0.0999070	+	0.994997i	$0.468145\pi$
$434$		0			0
$435$	−13.8974			−0.666331
$436$		0			0
$437$	22.8916	−	39.6494i	1.09505	−	1.89669i
$438$		0			0
$439$	0.340080	+	0.589036i	0.0162311	+	0.0281131i	0.874027	−	0.485878i	$-0.161500\pi$
$439$	0.340080	+	0.589036i	0.0162311	+	0.0281131i	−0.857796	+	0.513991i	$0.828167\pi$
$440$		0			0
$441$	−10.6284	−	5.04785i	−0.506115	−	0.240374i
$442$		0			0
$443$	−12.5590	−	21.7528i	−0.596696	−	1.03351i	−0.993305	−	0.115521i	$-0.963146\pi$
$443$	−12.5590	−	21.7528i	−0.596696	−	1.03351i	0.396609	−	0.917988i	$-0.370187\pi$
$444$		0			0
$445$	−6.75355	+	11.6975i	−0.320149	+	0.554514i
$446$		0			0
$447$	22.3858			1.05881
$448$		0			0
$449$	−27.8969			−1.31653			−0.658267	−	0.752784i	$-0.728710\pi$
$449$	−27.8969			−1.31653			−0.658267	+	0.752784i	$0.728710\pi$
$450$		0			0
$451$	0.779646	−	1.35039i	0.0367121	−	0.0635872i
$452$		0			0
$453$	−4.15016	−	7.18830i	−0.194992	−	0.337736i
$454$		0			0
$455$	14.6502	+	13.5199i	0.686810	+	0.633824i
$456$		0			0
$457$	3.85829	+	6.68275i	0.180483	+	0.312606i	0.942045	−	0.335486i	$-0.108901\pi$
$457$	3.85829	+	6.68275i	0.180483	+	0.312606i	−0.761562	+	0.648092i	$0.775567\pi$
$458$		0			0
$459$	2.96331	−	5.13261i	0.138316	−	0.239570i
$460$		0			0
$461$	30.2468			1.40874			0.704368	−	0.709835i	$-0.251231\pi$
$461$	30.2468			1.40874			0.704368	+	0.709835i	$0.251231\pi$
$462$		0			0
$463$	19.0380			0.884770			0.442385	−	0.896825i	$-0.354133\pi$
$463$	19.0380			0.884770			0.442385	+	0.896825i	$0.354133\pi$
$464$		0			0
$465$	−6.49922	+	11.2570i	−0.301394	+	0.522030i
$466$		0			0
$467$	−9.58148	−	16.5956i	−0.443378	−	0.767953i	0.554560	−	0.832144i	$-0.312887\pi$
$467$	−9.58148	−	16.5956i	−0.443378	−	0.767953i	−0.997938	+	0.0641906i	$0.979553\pi$
$468$		0			0
$469$	−6.81997	+	30.2566i	−0.314917	+	1.39712i
$470$		0			0
$471$	5.18409	+	8.97911i	0.238870	+	0.413736i
$472$		0			0
$473$	−2.58177	+	4.47175i	−0.118710	+	0.205611i
$474$		0			0
$475$	49.1080			2.25323
$476$		0			0
$477$	−10.7094			−0.490352
$478$		0			0
$479$	−18.4223	+	31.9084i	−0.841738	+	1.45793i	0.0466858	+	0.998910i	$0.485134\pi$
$479$	−18.4223	+	31.9084i	−0.841738	+	1.45793i	−0.888424	+	0.459024i	$0.848199\pi$
$480$		0			0
$481$	3.20776	+	5.55600i	0.146261	+	0.253332i
$482$		0			0
$483$	36.3233	−	11.3118i	1.65277	−	0.514703i
$484$		0			0
$485$	−6.86227	−	11.8858i	−0.311600	−	0.539706i
$486$		0			0
$487$	9.28014	−	16.0737i	0.420523	−	0.728368i	−0.575467	−	0.817825i	$-0.695180\pi$
$487$	9.28014	−	16.0737i	0.420523	−	0.728368i	0.995991	+	0.0894571i	$0.0285132\pi$
$488$		0			0
$489$	−17.0830			−0.772521
$490$		0			0
$491$	−41.9807			−1.89456			−0.947282	−	0.320400i	$-0.896183\pi$
$491$	−41.9807			−1.89456			−0.947282	+	0.320400i	$0.896183\pi$
$492$		0			0
$493$	−1.91511	+	3.31706i	−0.0862521	+	0.149393i
$494$		0			0
$495$	2.92697	+	5.06966i	0.131558	+	0.227864i
$496$		0			0
$497$	5.24580	−	1.63364i	0.235306	−	0.0732787i
$498$		0			0
$499$	−5.35545	−	9.27591i	−0.239743	−	0.415247i	0.720898	−	0.693042i	$-0.243730\pi$
$499$	−5.35545	−	9.27591i	−0.239743	−	0.415247i	−0.960640	+	0.277795i	$0.910396\pi$
$500$		0			0
$501$	−17.0871	+	29.5957i	−0.763394	+	1.32224i
$502$		0			0
$503$	13.2378			0.590243			0.295122	−	0.955460i	$-0.404640\pi$
$503$	13.2378			0.590243			0.295122	+	0.955460i	$0.404640\pi$
$504$		0			0
$505$	−19.4245			−0.864377
$506$		0			0
$507$	8.99935	−	15.5873i	0.399675	−	0.692258i
$508$		0			0
$509$	−14.9006	−	25.8086i	−0.660457	−	1.14395i	−0.980496	−	0.196541i	$-0.937029\pi$
$509$	−14.9006	−	25.8086i	−0.660457	−	1.14395i	0.320038	−	0.947405i	$-0.396304\pi$
$510$		0			0
$511$	8.09014	−	35.8917i	0.357887	−	1.58775i
$512$		0			0
$513$	9.82991	+	17.0259i	0.434001	+	0.751712i
$514$		0			0
$515$	28.2960	−	49.0101i	1.24687	−	2.15964i
$516$		0			0
$517$	−12.5081			−0.550105
$518$		0			0
$519$	−4.12343			−0.180999
$520$		0			0
$521$	−11.6075	+	20.1048i	−0.508534	+	0.880806i	0.491418	+	0.870924i	$0.336479\pi$
$521$	−11.6075	+	20.1048i	−0.508534	+	0.880806i	−0.999951	+	0.00988201i	$0.996854\pi$
$522$		0			0
$523$	12.1694	+	21.0781i	0.532132	+	0.921680i	0.999296	+	0.0375096i	$0.0119425\pi$
$523$	12.1694	+	21.0781i	0.532132	+	0.921680i	−0.467164	+	0.884171i	$0.654724\pi$
$524$		0			0
$525$	29.9883	+	27.6747i	1.30880	+	1.20782i
$526$		0			0
$527$	1.79122	+	3.10249i	0.0780269	+	0.135147i
$528$		0			0
$529$	−10.5859	+	18.3353i	−0.460255	+	0.797186i
$530$		0			0
$531$	21.4029			0.928806
$532$		0			0
$533$	3.37358			0.146126
$534$		0			0
$535$	−3.99573	+	6.92081i	−0.172751	+	0.299213i
$536$		0			0
$537$	−16.5703	−	28.7006i	−0.715062	−	1.23852i
$538$		0			0
$539$	0.560799	+	6.97750i	0.0241553	+	0.300542i
$540$		0			0
$541$	2.42078	+	4.19292i	0.104078	+	0.180268i	0.913361	−	0.407151i	$-0.133478\pi$
$541$	2.42078	+	4.19292i	0.104078	+	0.180268i	−0.809283	+	0.587418i	$0.800144\pi$
$542$		0			0
$543$	−23.3608	+	40.4620i	−1.00251	+	1.73639i
$544$		0			0
$545$	−39.8196			−1.70569
$546$		0			0
$547$	−25.3610			−1.08436			−0.542180	−	0.840262i	$-0.682401\pi$
$547$	−25.3610			−1.08436			−0.542180	+	0.840262i	$0.682401\pi$
$548$		0			0
$549$	−11.6210	+	20.1282i	−0.495972	+	0.859049i
$550$		0			0
$551$	−6.35280	−	11.0034i	−0.270638	−	0.468759i
$552$		0			0
$553$	7.33985	+	6.77360i	0.312122	+	0.288043i
$554$		0			0
$555$	11.1715	+	19.3496i	0.474204	+	0.821345i
$556$		0			0
$557$	15.2762	−	26.4591i	0.647272	−	1.12111i	−0.336500	−	0.941683i	$-0.609243\pi$
$557$	15.2762	−	26.4591i	0.647272	−	1.12111i	0.983772	−	0.179424i	$-0.0574233\pi$
$558$		0			0
$559$	−11.1715			−0.472504
$560$		0			0
$561$	4.49289			0.189690
$562$		0			0
$563$	−5.13708	+	8.89768i	−0.216502	+	0.374993i	−0.953736	−	0.300645i	$-0.902798\pi$
$563$	−5.13708	+	8.89768i	−0.216502	+	0.374993i	0.737234	+	0.675637i	$0.236131\pi$
$564$		0			0
$565$	−12.9267	−	22.3897i	−0.543830	−	0.941941i
$566$		0			0
$567$	−6.52586	+	28.9518i	−0.274060	+	1.21586i
$568$		0			0
$569$	1.59798	+	2.76778i	0.0669907	+	0.116031i	0.897575	−	0.440861i	$-0.145327\pi$
$569$	1.59798	+	2.76778i	0.0669907	+	0.116031i	−0.830585	+	0.556892i	$0.811994\pi$
$570$		0			0
$571$	−15.7208	+	27.2292i	−0.657894	+	1.13951i	0.323266	+	0.946308i	$0.395219\pi$
$571$	−15.7208	+	27.2292i	−0.657894	+	1.13951i	−0.981160	+	0.193197i	$0.938114\pi$
$572$		0			0
$573$	7.75357			0.323910
$574$		0			0
$575$	−47.3795			−1.97586
$576$		0			0
$577$	4.31370	−	7.47155i	0.179582	−	0.311045i	−0.762156	−	0.647394i	$-0.775859\pi$
$577$	4.31370	−	7.47155i	0.179582	−	0.311045i	0.941737	+	0.336349i	$0.109192\pi$
$578$		0			0
$579$	−8.51399	−	14.7467i	−0.353829	−	0.612851i
$580$		0			0
$581$	−12.7364	+	3.96635i	−0.528395	+	0.164552i
$582$		0			0
$583$	3.18565	+	5.51770i	0.131936	+	0.228520i
$584$		0			0
$585$	−6.33261	+	10.9684i	−0.261821	+	0.453488i
$586$		0			0
$587$	−17.8187			−0.735455			−0.367728	−	0.929934i	$-0.619864\pi$
$587$	−17.8187			−0.735455			−0.367728	+	0.929934i	$0.619864\pi$
$588$		0			0
$589$	−11.8837			−0.489659
$590$		0			0
$591$	19.5172	−	33.8048i	0.802830	−	1.39054i
$592$		0			0
$593$	17.8698	+	30.9514i	0.733824	+	1.27102i	0.955237	+	0.295841i	$0.0955998\pi$
$593$	17.8698	+	30.9514i	0.733824	+	1.27102i	−0.221413	+	0.975180i	$0.571067\pi$
$594$		0			0
$595$	18.2693	−	5.68939i	0.748967	−	0.233242i
$596$		0			0
$597$	−28.2732	−	48.9705i	−1.15714	−	2.00423i
$598$		0			0
$599$	15.1143	−	26.1788i	0.617554	−	1.06964i	−0.372376	−	0.928082i	$-0.621457\pi$
$599$	15.1143	−	26.1788i	0.617554	−	1.06964i	0.989931	−	0.141553i	$-0.0452097\pi$
$600$		0			0
$601$	34.0674			1.38964			0.694819	−	0.719185i	$-0.255485\pi$
$601$	34.0674			1.38964			0.694819	+	0.719185i	$0.255485\pi$
$602$		0			0
$603$	−19.7048			−0.802440
$604$		0			0
$605$	1.74132	−	3.01606i	0.0707949	−	0.122620i
$606$		0			0
$607$	7.11468	+	12.3230i	0.288776	+	0.500175i	0.973518	−	0.228611i	$-0.0734184\pi$
$607$	7.11468	+	12.3230i	0.288776	+	0.500175i	−0.684742	+	0.728786i	$0.740085\pi$
$608$		0			0
$609$	2.32154	−	10.2994i	0.0940733	−	0.417354i
$610$		0			0
$611$	−13.5309	−	23.4361i	−0.547400	−	0.948124i
$612$		0			0
$613$	−4.21572	+	7.30185i	−0.170271	+	0.294919i	−0.938515	−	0.345239i	$-0.887798\pi$
$613$	−4.21572	+	7.30185i	−0.170271	+	0.294919i	0.768243	+	0.640158i	$0.221131\pi$
$614$		0			0
$615$	11.7490			0.473765
$616$		0			0
$617$	33.3958			1.34446			0.672231	−	0.740341i	$-0.265336\pi$
$617$	33.3958			1.34446			0.672231	+	0.740341i	$0.265336\pi$
$618$		0			0
$619$	17.9907	−	31.1609i	0.723109	−	1.25246i	−0.236639	−	0.971598i	$-0.576046\pi$
$619$	17.9907	−	31.1609i	0.723109	−	1.25246i	0.959748	−	0.280863i	$-0.0906208\pi$
$620$		0			0
$621$	−9.48392	−	16.4266i	−0.380576	−	0.659178i
$622$		0			0
$623$	−7.54087	−	6.95911i	−0.302119	−	0.278811i
$624$		0			0
$625$	4.91196	+	8.50777i	0.196479	+	0.340311i
$626$		0			0
$627$	−7.45192	+	12.9071i	−0.297601	+	0.515460i
$628$		0			0
$629$	6.15786			0.245530
$630$		0			0
$631$	1.38624			0.0551852			0.0275926	−	0.999619i	$-0.491216\pi$
$631$	1.38624			0.0551852			0.0275926	+	0.999619i	$0.491216\pi$
$632$		0			0
$633$	−17.5870	+	30.4616i	−0.699021	+	1.21074i
$634$		0			0
$635$	15.4740	+	26.8018i	0.614068	+	1.06360i
$636$		0			0
$637$	−12.4669	+	8.59879i	−0.493958	+	0.340697i
$638$		0			0
$639$	1.74530	+	3.02296i	0.0690432	+	0.119586i
$640$		0			0
$641$	24.3781	−	42.2241i	0.962878	−	1.66775i	0.247666	−	0.968846i	$-0.420337\pi$
$641$	24.3781	−	42.2241i	0.962878	−	1.66775i	0.715212	−	0.698907i	$-0.246330\pi$
$642$		0			0
$643$	21.1051			0.832304			0.416152	−	0.909295i	$-0.363378\pi$
$643$	21.1051			0.832304			0.416152	+	0.909295i	$0.363378\pi$
$644$		0			0
$645$	−38.9064			−1.53194
$646$		0			0
$647$	−10.9385	+	18.9461i	−0.430039	+	0.744849i	−0.996876	−	0.0789807i	$-0.974833\pi$
$647$	−10.9385	+	18.9461i	−0.430039	+	0.744849i	0.566837	+	0.823830i	$0.308167\pi$
$648$		0			0
$649$	−6.36654	−	11.0272i	−0.249908	−	0.432854i
$650$		0			0
$651$	−7.25689	−	6.69704i	−0.284420	−	0.262478i
$652$		0			0
$653$	24.5801	+	42.5740i	0.961894	+	1.66605i	0.717739	+	0.696313i	$0.245177\pi$
$653$	24.5801	+	42.5740i	0.961894	+	1.66605i	0.244155	+	0.969736i	$0.421489\pi$
$654$		0			0
$655$	10.2362	−	17.7296i	0.399961	−	0.692753i
$656$		0			0
$657$	23.3747			0.911933
$658$		0			0
$659$	5.33789			0.207935			0.103967	−	0.994581i	$-0.466846\pi$
$659$	5.33789			0.207935			0.103967	+	0.994581i	$0.466846\pi$
$660$		0			0
$661$	16.1807	−	28.0258i	0.629357	−	1.09008i	−0.358323	−	0.933598i	$-0.616651\pi$
$661$	16.1807	−	28.0258i	0.629357	−	1.09008i	0.987681	−	0.156482i	$-0.0500152\pi$
$662$		0			0
$663$	4.86027	+	8.41824i	0.188757	+	0.326937i
$664$		0			0
$665$	−13.9570	+	61.9200i	−0.541231	+	2.40116i
$666$		0			0
$667$	6.12920	+	10.6161i	0.237323	+	0.411056i
$668$		0			0
$669$	−15.9267	+	27.5858i	−0.615761	+	1.06653i
$670$		0			0
$671$	13.8272			0.533793
$672$		0			0
$673$	36.6083			1.41115			0.705574	−	0.708636i	$-0.250689\pi$
$673$	36.6083			1.41115			0.705574	+	0.708636i	$0.250689\pi$
$674$		0			0
$675$	10.1726	−	17.6195i	0.391545	−	0.678176i
$676$		0			0
$677$	−10.3908	−	17.9975i	−0.399352	−	0.691698i	0.594294	−	0.804248i	$-0.297432\pi$
$677$	−10.3908	−	17.9975i	−0.399352	−	0.691698i	−0.993646	+	0.112550i	$0.964098\pi$
$678$		0			0
$679$	9.95492	−	3.10015i	0.382035	−	0.118973i
$680$		0			0
$681$	−20.3853	−	35.3084i	−0.781166	−	1.35302i
$682$		0			0
$683$	−0.898465	+	1.55619i	−0.0343788	+	0.0595459i	−0.882703	−	0.469932i	$-0.844279\pi$
$683$	−0.898465	+	1.55619i	−0.0343788	+	0.0595459i	0.848324	+	0.529477i	$0.177612\pi$
$684$		0			0
$685$	−63.9153			−2.44208
$686$		0			0
$687$	−44.3872			−1.69348
$688$		0			0
$689$	−6.89227	+	11.9378i	−0.262574	+	0.454792i
$690$		0			0
$691$	13.2872	+	23.0141i	0.505468	+	0.875497i	0.999980	+	0.00632576i	$0.00201356\pi$
$691$	13.2872	+	23.0141i	0.505468	+	0.875497i	−0.494512	+	0.869171i	$0.664653\pi$
$692$		0			0
$693$	−4.24608	+	1.32231i	−0.161295	+	0.0502304i
$694$		0			0
$695$	−37.9478	−	65.7275i	−1.43944	−	2.49319i
$696$		0			0
$697$	1.61905	−	2.80427i	0.0613258	−	0.106219i
$698$		0			0
$699$	−55.5058			−2.09942
$700$		0			0
$701$	−7.79947			−0.294582			−0.147291	−	0.989093i	$-0.547055\pi$
$701$	−7.79947			−0.294582			−0.147291	+	0.989093i	$0.547055\pi$
$702$		0			0
$703$	−10.2134	+	17.6902i	−0.385207	+	0.667198i
$704$		0			0
$705$	−47.1232	−	81.6197i	−1.77476	−	3.07398i
$706$		0			0
$707$	3.24481	−	14.3955i	0.122034	−	0.541399i
$708$		0			0
$709$	−13.7584	−	23.8303i	−0.516709	−	0.894966i	−0.999812	−	0.0194026i	$-0.993824\pi$
$709$	−13.7584	−	23.8303i	−0.516709	−	0.894966i	0.483103	−	0.875564i	$-0.339510\pi$
$710$		0			0
$711$	−3.17269	+	5.49526i	−0.118985	+	0.206088i
$712$		0			0
$713$	11.4654			0.429383
$714$		0			0
$715$	7.53483			0.281787
$716$		0			0
$717$	−22.8122	+	39.5119i	−0.851937	+	1.47560i
$718$		0			0
$719$	1.49090	+	2.58231i	0.0556010	+	0.0963038i	0.892486	−	0.451075i	$-0.148959\pi$
$719$	1.49090	+	2.58231i	0.0556010	+	0.0963038i	−0.836885	+	0.547378i	$0.815626\pi$
$720$		0			0
$721$	31.5947	+	29.1572i	1.17665	+	1.08587i
$722$		0			0
$723$	−12.8419	−	22.2427i	−0.477594	−	0.827216i
$724$		0			0
$725$	−6.57430	+	11.3870i	−0.244163	+	0.422903i
$726$		0			0
$727$	−40.4981			−1.50199			−0.750996	−	0.660307i	$-0.770426\pi$
$727$	−40.4981			−1.50199			−0.750996	+	0.660307i	$0.770426\pi$
$728$		0			0
$729$	−0.331170			−0.0122656
$730$		0			0
$731$	−5.36141	+	9.28624i	−0.198299	+	0.343464i
$732$		0			0
$733$	10.8161	+	18.7341i	0.399502	+	0.691958i	0.993665	−	0.112387i	$-0.0358496\pi$
$733$	10.8161	+	18.7341i	0.399502	+	0.691958i	−0.594162	+	0.804345i	$0.702516\pi$
$734$		0			0
$735$	−43.4179	+	29.9466i	−1.60149	+	1.10460i
$736$		0			0
$737$	5.86141	+	10.1523i	0.215908	+	0.373964i
$738$		0			0
$739$	9.06369	−	15.6988i	0.333413	−	0.577488i	−0.649766	−	0.760135i	$-0.725133\pi$
$739$	9.06369	−	15.6988i	0.333413	−	0.577488i	0.983179	+	0.182646i	$0.0584663\pi$
$740$		0			0
$741$	−32.2450			−1.18455
$742$		0			0
$743$	6.77428			0.248524			0.124262	−	0.992249i	$-0.460344\pi$
$743$	6.77428			0.248524			0.124262	+	0.992249i	$0.460344\pi$
$744$		0			0
$745$	18.0172	−	31.2067i	0.660099	−	1.14332i
$746$		0			0
$747$	−4.23747	−	7.33951i	−0.155041	−	0.268539i
$748$		0			0
$749$	−4.46155	−	4.11735i	−0.163022	−	0.150445i
$750$		0			0
$751$	5.13781	+	8.89894i	0.187481	+	0.324727i	0.944410	−	0.328771i	$-0.106634\pi$
$751$	5.13781	+	8.89894i	0.187481	+	0.324727i	−0.756929	+	0.653498i	$0.773301\pi$
$752$		0			0
$753$	3.83248	−	6.63805i	0.139663	−	0.241904i
$754$		0			0
$755$	−13.3610			−0.486258
$756$		0			0
$757$	−48.5477			−1.76450			−0.882249	−	0.470783i	$-0.843971\pi$
$757$	−48.5477			−1.76450			−0.882249	+	0.470783i	$0.843971\pi$
$758$		0			0
$759$	7.18963	−	12.4528i	0.260967	−	0.452008i
$760$		0			0
$761$	0.0119427	+	0.0206854i	0.000432924	+	0.000749846i	0.866242	−	0.499625i	$-0.166529\pi$
$761$	0.0119427	+	0.0206854i	0.000432924	+	0.000749846i	−0.865809	+	0.500375i	$0.833196\pi$
$762$		0			0
$763$	6.65178	−	29.5104i	0.240811	−	1.06835i
$764$		0			0
$765$	6.07828	+	10.5279i	0.219761	+	0.380637i
$766$		0			0
$767$	13.7742	−	23.8577i	0.497359	−	0.861451i
$768$		0			0
$769$	−30.3283			−1.09367			−0.546833	−	0.837241i	$-0.684167\pi$
$769$	−30.3283			−1.09367			−0.546833	+	0.837241i	$0.684167\pi$
$770$		0			0
$771$	27.4583			0.988886
$772$		0			0
$773$	10.7287	−	18.5827i	0.385886	−	0.668373i	−0.606006	−	0.795460i	$-0.707229\pi$
$773$	10.7287	−	18.5827i	0.385886	−	0.668373i	0.991892	+	0.127087i	$0.0405626\pi$
$774$		0			0
$775$	6.14902	+	10.6504i	0.220879	+	0.382574i
$776$		0			0
$777$	−16.2062	+	5.04691i	−0.581394	+	0.181057i
$778$		0			0
$779$	5.37071	+	9.30233i	0.192425	+	0.333291i
$780$		0			0
$781$	1.03832	−	1.79843i	0.0371541	−	0.0643528i
$782$		0			0
$783$	−5.26389			−0.188116
$784$		0			0
$785$	16.6897			0.595680
$786$		0			0
$787$	12.7110	−	22.0160i	0.453097	−	0.784787i	−0.545480	−	0.838124i	$-0.683652\pi$
$787$	12.7110	−	22.0160i	0.453097	−	0.784787i	0.998577	+	0.0533372i	$0.0169858\pi$
$788$		0			0
$789$	−1.50127	−	2.60028i	−0.0534466	−	0.0925723i
$790$		0			0
$791$	18.7524	−	5.83985i	0.666759	−	0.207641i
$792$		0			0
$793$	14.9578	+	25.9077i	0.531168	+	0.920010i
$794$		0			0
$795$	−24.0033	+	41.5750i	−0.851310	+	1.47451i
$796$		0			0
$797$	−39.7648			−1.40854			−0.704270	−	0.709932i	$-0.748726\pi$
$797$	−39.7648			−1.40854			−0.704270	+	0.709932i	$0.748726\pi$
$798$		0			0
$799$	−25.9749			−0.918924
$800$		0			0
$801$	3.25958	−	5.64576i	0.115172	−	0.199483i
$802$		0			0
$803$	−6.95307	−	12.0431i	−0.245368	−	0.424990i
$804$		0			0
$805$	13.4658	−	59.7406i	0.474607	−	2.10558i
$806$		0			0
$807$	−0.0564534	−	0.0977801i	−0.00198725	−	0.00344202i
$808$		0			0
$809$	−4.44107	+	7.69217i	−0.156140	+	0.270442i	−0.933473	−	0.358646i	$-0.883238\pi$
$809$	−4.44107	+	7.69217i	−0.156140	+	0.270442i	0.777334	+	0.629089i	$0.216572\pi$
$810$		0			0
$811$	28.0515			0.985020			0.492510	−	0.870307i	$-0.336080\pi$
$811$	28.0515			0.985020			0.492510	+	0.870307i	$0.336080\pi$
$812$		0			0
$813$	33.3520			1.16971
$814$		0			0
$815$	−13.7493	+	23.8145i	−0.481616	+	0.834184i
$816$		0			0
$817$	−17.7849	−	30.8043i	−0.622215	−	1.07771i
$818$		0			0
$819$	−7.07086	−	6.52536i	−0.247076	−	0.228014i
$820$		0			0
$821$	7.59478	+	13.1545i	0.265059	+	0.459097i	0.967579	−	0.252568i	$-0.0812751\pi$
$821$	7.59478	+	13.1545i	0.265059	+	0.459097i	−0.702520	+	0.711664i	$0.747942\pi$
$822$		0			0
$823$	4.44006	−	7.69041i	0.154771	−	0.268071i	−0.778205	−	0.628011i	$-0.783869\pi$
$823$	4.44006	−	7.69041i	0.154771	−	0.268071i	0.932976	+	0.359940i	$0.117203\pi$
$824$		0			0
$825$	15.4235			0.536977
$826$		0			0
$827$	41.6292			1.44759			0.723795	−	0.690015i	$-0.242396\pi$
$827$	41.6292			1.44759			0.723795	+	0.690015i	$0.242396\pi$
$828$		0			0
$829$	3.81170	−	6.60206i	0.132386	−	0.229299i	−0.792210	−	0.610249i	$-0.791070\pi$
$829$	3.81170	−	6.60206i	0.132386	−	0.229299i	0.924596	+	0.380950i	$0.124403\pi$
$830$		0			0
$831$	9.81821	+	17.0056i	0.340590	+	0.589919i
$832$		0			0
$833$	1.16458	+	14.4898i	0.0403503	+	0.502041i
$834$		0			0
$835$	27.5051	+	47.6402i	0.951853	+	1.64866i
$836$		0			0
$837$	−2.46169	+	4.26377i	−0.0850884	+	0.147377i
$838$		0			0
$839$	46.6316			1.60990			0.804951	−	0.593341i	$-0.202191\pi$
$839$	46.6316			1.60990			0.804951	+	0.593341i	$0.202191\pi$
$840$		0			0
$841$	−25.5981			−0.882693
$842$		0			0
$843$	−15.3884	+	26.6535i	−0.530005	+	0.917996i
$844$		0			0
$845$	−14.4863	−	25.0909i	−0.498343	−	0.863155i
$846$		0			0
$847$	1.94432	+	1.79432i	0.0668078	+	0.0616537i
$848$		0			0
$849$	16.5514	+	28.6679i	0.568043	+	0.983879i
$850$		0			0
$851$	9.85394	−	17.0675i	0.337789	−	0.585067i
$852$		0			0
$853$	20.6587			0.707341			0.353671	−	0.935370i	$-0.384933\pi$
$853$	20.6587			0.707341			0.353671	+	0.935370i	$0.384933\pi$
$854$		0			0
$855$	−40.3258			−1.37911
$856$		0			0
$857$	13.2300	−	22.9149i	0.451927	−	0.782760i	−0.546579	−	0.837407i	$-0.684070\pi$
$857$	13.2300	−	22.9149i	0.451927	−	0.782760i	0.998506	+	0.0546477i	$0.0174036\pi$
$858$		0			0
$859$	−20.8647	−	36.1388i	−0.711896	−	1.23304i	−0.964145	−	0.265377i	$-0.914503\pi$
$859$	−20.8647	−	36.1388i	−0.711896	−	1.23304i	0.252249	−	0.967662i	$-0.418830\pi$
$860$		0			0
$861$	−1.96264	+	8.70721i	−0.0668867	+	0.296741i
$862$		0			0
$863$	3.01621	+	5.22423i	0.102673	+	0.177835i	0.912785	−	0.408440i	$-0.133927\pi$
$863$	3.01621	+	5.22423i	0.102673	+	0.177835i	−0.810112	+	0.586275i	$0.800594\pi$
$864$		0			0
$865$	−3.31875	+	5.74824i	−0.112841	+	0.195446i
$866$		0			0
$867$	−27.4500			−0.932250
$868$		0			0
$869$	3.77501			0.128059
$870$		0			0
$871$	−12.6814	+	21.9648i	−0.429692	+	0.744249i
$872$		0			0
$873$	3.31205	+	5.73665i	0.112096	+	0.194156i
$874$		0			0
$875$	18.7284	−	5.83236i	0.633134	−	0.197170i
$876$		0			0
$877$	9.09165	+	15.7472i	0.307003	+	0.531745i	0.977705	−	0.209982i	$-0.0673404\pi$
$877$	9.09165	+	15.7472i	0.307003	+	0.531745i	−0.670702	+	0.741727i	$0.734007\pi$
$878$		0			0
$879$	14.8295	−	25.6855i	0.500188	−	0.866351i
$880$		0			0
$881$	24.1496			0.813620			0.406810	−	0.913513i	$-0.366641\pi$
$881$	24.1496			0.813620			0.406810	+	0.913513i	$0.366641\pi$
$882$		0			0
$883$	13.1843			0.443687			0.221843	−	0.975082i	$-0.428793\pi$
$883$	13.1843			0.443687			0.221843	+	0.975082i	$0.428793\pi$
$884$		0			0
$885$	47.9708	−	83.0879i	1.61252	−	2.79297i
$886$		0			0
$887$	5.36589	+	9.29399i	0.180169	+	0.312062i	0.941938	−	0.335787i	$-0.109002\pi$
$887$	5.36589	+	9.29399i	0.180169	+	0.312062i	−0.761769	+	0.647849i	$0.775669\pi$
$888$		0			0
$889$	−22.4478	+	6.99066i	−0.752874	+	0.234459i
$890$		0			0
$891$	5.60864	+	9.71445i	0.187896	+	0.325446i
$892$		0			0
$893$	43.0819	−	74.6201i	1.44168	−	2.49707i
$894$		0			0
$895$	−53.3465			−1.78318
$896$		0			0
$897$	31.1100			1.03873
$898$		0			0
$899$	1.59092	−	2.75556i	0.0530602	−	0.0919030i
$900$		0			0
$901$	6.61546	+	11.4583i	0.220393	+	0.381732i
$902$		0			0
$903$	6.49922	−	28.8336i	0.216281	−	0.959522i
$904$		0			0
$905$	37.6038	+	65.1318i	1.24999	+	2.16505i
$906$		0			0
$907$	−17.7247	+	30.7002i	−0.588541	+	1.01938i	0.405883	+	0.913925i	$0.366964\pi$
$907$	−17.7247	+	30.7002i	−0.588541	+	1.01938i	−0.994424	+	0.105457i	$0.966369\pi$
$908$		0			0
$909$	9.37516			0.310954
$910$		0			0
$911$	−37.4277			−1.24004			−0.620018	−	0.784588i	$-0.712875\pi$
$911$	−37.4277			−1.24004			−0.620018	+	0.784588i	$0.712875\pi$
$912$		0			0
$913$	−2.52097	+	4.36645i	−0.0834319	+	0.144508i
$914$		0			0
$915$	52.0928	+	90.2274i	1.72214	+	2.98283i
$916$		0			0
$917$	11.4295	+	10.5478i	0.377436	+	0.348318i
$918$		0			0
$919$	0.370932	+	0.642473i	0.0122359	+	0.0211932i	0.872079	−	0.489366i	$-0.162772\pi$
$919$	0.370932	+	0.642473i	0.0122359	+	0.0211932i	−0.859843	+	0.510559i	$0.829438\pi$
$920$		0			0
$921$	33.2336	−	57.5622i	1.09508	−	1.89674i
$922$		0			0
$923$	4.49289			0.147885
$924$		0			0
$925$	21.1391			0.695049
$926$		0			0
$927$	−13.6570	+	23.6546i	−0.448554	+	0.776918i
$928$		0			0
$929$	12.0365	+	20.8478i	0.394904	+	0.683993i	0.993089	−	0.117365i	$-0.0374446\pi$
$929$	12.0365	+	20.8478i	0.394904	+	0.683993i	−0.598185	+	0.801358i	$0.704111\pi$
$930$		0			0
$931$	−43.5576	−	20.6872i	−1.42754	−	0.677995i
$932$		0			0
$933$	−11.0235	−	19.0933i	−0.360894	−	0.625087i
$934$		0			0
$935$	3.61611	−	6.26329i	0.118259	−	0.204831i
$936$		0			0
$937$	35.2057			1.15012			0.575061	−	0.818111i	$-0.304978\pi$
$937$	35.2057			1.15012			0.575061	+	0.818111i	$0.304978\pi$
$938$		0			0
$939$	21.5775			0.704155
$940$		0			0
$941$	9.73555	−	16.8625i	0.317370	−	0.549701i	−0.662569	−	0.749001i	$-0.730534\pi$
$941$	9.73555	−	16.8625i	0.317370	−	0.549701i	0.979938	+	0.199301i	$0.0638670\pi$
$942$		0			0
$943$	−5.18167	−	8.97491i	−0.168738	−	0.292263i
$944$		0			0
$945$	19.3252	+	17.8343i	0.628648	+	0.580150i
$946$		0			0
$947$	13.0961	+	22.6832i	0.425567	+	0.737103i	0.996473	−	0.0839118i	$-0.0267414\pi$
$947$	13.0961	+	22.6832i	0.425567	+	0.737103i	−0.570906	+	0.821015i	$0.693408\pi$
$948$		0			0
$949$	15.0432	−	26.0556i	0.488323	−	0.845801i
$950$		0			0
$951$	−51.0486			−1.65536
$952$		0			0
$953$	−20.2167			−0.654883			−0.327442	−	0.944871i	$-0.606186\pi$
$953$	−20.2167			−0.654883			−0.327442	+	0.944871i	$0.606186\pi$
$954$		0			0
$955$	6.24047	−	10.8088i	0.201937	−	0.349765i
$956$		0			0
$957$	−1.99524	−	3.45586i	−0.0644970	−	0.111712i
$958$		0			0
$959$	10.6769	−	47.3678i	0.344775	−	1.52959i
$960$		0			0
$961$	14.0120	+	24.2695i	0.452000	+	0.782886i
$962$		0			0
$963$	1.92853	−	3.34031i	0.0621460	−	0.107640i
$964$		0			0
$965$	−27.4100			−0.882358
$966$		0			0
$967$	−0.615223			−0.0197842			−0.00989211	−	0.999951i	$-0.503149\pi$
$967$	−0.615223			−0.0197842			−0.00989211	+	0.999951i	$0.503149\pi$
$968$		0			0
$969$	−15.4750	+	26.8035i	−0.497128	+	0.861051i
$970$		0			0
$971$	−14.0999	−	24.4217i	−0.452487	−	0.783731i	0.546053	−	0.837751i	$-0.316130\pi$
$971$	−14.0999	−	24.4217i	−0.452487	−	0.783731i	−0.998540	+	0.0540199i	$0.982797\pi$
$972$		0			0
$973$	55.0499	−	17.1436i	1.76482	−	0.549597i
$974$		0			0
$975$	16.6846	+	28.8986i	0.534336	+	0.925497i
$976$		0			0
$977$	3.78201	−	6.55063i	0.120997	−	0.209573i	−0.799164	−	0.601113i	$-0.794724\pi$
$977$	3.78201	−	6.55063i	0.120997	−	0.209573i	0.920161	+	0.391540i	$0.128057\pi$
$978$		0			0
$979$	−3.87840			−0.123954
$980$		0			0
$981$	19.2188			0.613610
$982$		0			0
$983$	23.3498	−	40.4430i	0.744743	−	1.28993i	−0.205572	−	0.978642i	$-0.565905\pi$
$983$	23.3498	−	40.4430i	0.744743	−	1.28993i	0.950315	−	0.311291i	$-0.100761\pi$
$984$		0			0
$985$	−31.4169	−	54.4156i	−1.00102	−	1.73382i
$986$		0			0
$987$	68.3604	−	21.2887i	2.17594	−	0.677627i
$988$		0			0
$989$	17.1589	+	29.7201i	0.545621	+	0.945044i
$990$		0			0
$991$	26.6161	−	46.1004i	0.845488	−	1.46443i	−0.0397095	−	0.999211i	$-0.512643\pi$
$991$	26.6161	−	46.1004i	0.845488	−	1.46443i	0.885197	−	0.465216i	$-0.154023\pi$
$992$		0			0
$993$	−30.6249			−0.971851
$994$		0			0
$995$	−91.0227			−2.88561
$996$		0			0
$997$	−8.07899	+	13.9932i	−0.255864	+	0.443170i	−0.965130	−	0.261771i	$-0.915693\pi$
$997$	−8.07899	+	13.9932i	−0.255864	+	0.443170i	0.709266	+	0.704941i	$0.249027\pi$
$998$		0			0
$999$	4.23139	+	7.32899i	0.133875	+	0.231879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.n.529.2		8
4.3	odd	2		616.2.q.d.529.3	yes	8
7.2	even	3	inner	1232.2.q.n.177.2		8
7.3	odd	6		8624.2.a.cr.1.2		4
7.4	even	3		8624.2.a.cz.1.3		4
28.3	even	6		4312.2.a.bd.1.3		4
28.11	odd	6		4312.2.a.y.1.2		4
28.23	odd	6		616.2.q.d.177.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.d.177.3	✓	8	28.23	odd	6
616.2.q.d.529.3	yes	8	4.3	odd	2
1232.2.q.n.177.2		8	7.2	even	3	inner
1232.2.q.n.529.2		8	1.1	even	1	trivial
4312.2.a.y.1.2		4	28.11	odd	6
4312.2.a.bd.1.3		4	28.3	even	6
8624.2.a.cr.1.2		4	7.3	odd	6
8624.2.a.cz.1.3		4	7.4	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08177 + 1.87368i) q^{3} +(1.74132 + 3.01606i) q^{5} +(-2.52609 + 0.786673i) q^{7} +(-0.840445 - 1.45569i) q^{9} +O(q^{10})\)	\(q+(-1.08177 + 1.87368i) q^{3} +(1.74132 + 3.01606i) q^{5} +(-2.52609 + 0.786673i) q^{7} +(-0.840445 - 1.45569i) q^{9} +(-0.500000 + 0.866025i) q^{11} -2.16354 q^{13} -7.53483 q^{15} +(-1.03832 + 1.79843i) q^{17} +(-3.44432 - 5.96575i) q^{19} +(1.25868 - 5.58408i) q^{21} +(3.32309 + 5.75576i) q^{23} +(-3.56442 + 6.17375i) q^{25} -2.85394 q^{27} +1.84443 q^{29} +(0.862557 - 1.49399i) q^{31} +(-1.08177 - 1.87368i) q^{33} +(-6.77140 - 6.24900i) q^{35} +(-1.48265 - 2.56802i) q^{37} +(2.34044 - 4.05377i) q^{39} -1.55929 q^{41} +5.16354 q^{43} +(2.92697 - 5.06966i) q^{45} +(6.25404 + 10.8323i) q^{47} +(5.76229 - 3.97442i) q^{49} +(-2.24645 - 3.89096i) q^{51} +(3.18565 - 5.51770i) q^{53} -3.48265 q^{55} +14.9038 q^{57} +(-6.36654 + 11.0272i) q^{59} +(-6.91360 - 11.9747i) q^{61} +(3.26819 + 3.01606i) q^{63} +(-3.76742 - 6.52536i) q^{65} +(5.86141 - 10.1523i) q^{67} -14.3793 q^{69} -2.07664 q^{71} +(-6.95307 + 12.0431i) q^{73} +(-7.71174 - 13.3571i) q^{75} +(0.581768 - 2.58100i) q^{77} +(-1.88751 - 3.26926i) q^{79} +(5.60864 - 9.71445i) q^{81} +5.04194 q^{83} -7.23222 q^{85} +(-1.99524 + 3.45586i) q^{87} +(1.93920 + 3.35879i) q^{89} +(5.46529 - 1.70199i) q^{91} +(1.86617 + 3.23231i) q^{93} +(11.9954 - 20.7766i) q^{95} -3.94084 q^{97} +1.68089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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