LMFDB - Embedded newform 208.3.bd.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,3,Mod(33,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("208.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, 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:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.97
Dual form			208.3.bd.d.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 2.36603i) q^{3} +(-4.36603 + 4.36603i) q^{5} +(-2.26795 + 8.46410i) q^{7} +(0.767949 + 1.33013i) q^{9} +O(q^{10})$	\(q+(1.36603 - 2.36603i) q^{3} +(-4.36603 + 4.36603i) q^{5} +(-2.26795 + 8.46410i) q^{7} +(0.767949 + 1.33013i) q^{9} +(-6.19615 + 1.66025i) q^{11} +(-6.50000 + 11.2583i) q^{13} +(4.36603 + 16.2942i) q^{15} +(9.99038 - 5.76795i) q^{17} +(-3.36603 - 0.901924i) q^{19} +(16.9282 + 16.9282i) q^{21} +(8.49038 + 4.90192i) q^{23} -13.1244i q^{25} +28.7846 q^{27} +(5.69615 - 9.86603i) q^{29} +(-1.92820 + 1.92820i) q^{31} +(-4.53590 + 16.9282i) q^{33} +(-27.0526 - 46.8564i) q^{35} +(-42.1147 + 11.2846i) q^{37} +(17.7583 + 30.7583i) q^{39} +(5.08142 + 18.9641i) q^{41} +(-45.0000 + 25.9808i) q^{43} +(-9.16025 - 2.45448i) q^{45} +(-0.320508 - 0.320508i) q^{47} +(-24.0622 - 13.8923i) q^{49} -31.5167i q^{51} +78.7654 q^{53} +(19.8038 - 34.3013i) q^{55} +(-6.73205 + 6.73205i) q^{57} +(-10.9615 + 40.9090i) q^{59} +(-49.1865 - 85.1936i) q^{61} +(-13.0000 + 3.48334i) q^{63} +(-20.7750 - 77.5333i) q^{65} +(-19.9737 - 74.5429i) q^{67} +(23.1962 - 13.3923i) q^{69} +(31.0263 + 8.31347i) q^{71} +(48.2750 + 48.2750i) q^{73} +(-31.0526 - 17.9282i) q^{75} -56.2102i q^{77} +82.7461 q^{79} +(32.4090 - 56.1340i) q^{81} +(69.5167 - 69.5167i) q^{83} +(-18.4352 + 68.8013i) q^{85} +(-15.5622 - 26.9545i) q^{87} +(-31.8301 + 8.52886i) q^{89} +(-80.5500 - 80.5500i) q^{91} +(1.92820 + 7.19615i) q^{93} +(18.6340 - 10.7583i) q^{95} +(74.8109 + 20.0455i) q^{97} +(-6.96668 - 6.96668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9	$ 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9} - 4 q^{11} - 26 q^{13} + 14 q^{15} - 12 q^{17} - 10 q^{19} + 40 q^{21} - 18 q^{23} + 32 q^{27} + 2 q^{29} + 20 q^{31} - 32 q^{33} - 32 q^{35} - 68 q^{37} + 26 q^{39} + 100 q^{41} - 180 q^{43} - 2 q^{45} + 68 q^{47} - 72 q^{49} + 128 q^{53} + 100 q^{55} - 20 q^{57} + 164 q^{59} - 124 q^{61} - 52 q^{63} + 52 q^{65} - 118 q^{67} + 72 q^{69} + 86 q^{71} + 58 q^{73} - 48 q^{75} + 40 q^{79} - 2 q^{81} + 188 q^{83} + 96 q^{85} - 38 q^{87} - 110 q^{89} - 52 q^{91} - 20 q^{93} + 78 q^{95} + 178 q^{97} - 208 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9 - 4 * q^11 - 26 * q^13 + 14 * q^15 - 12 * q^17 - 10 * q^19 + 40 * q^21 - 18 * q^23 + 32 * q^27 + 2 * q^29 + 20 * q^31 - 32 * q^33 - 32 * q^35 - 68 * q^37 + 26 * q^39 + 100 * q^41 - 180 * q^43 - 2 * q^45 + 68 * q^47 - 72 * q^49 + 128 * q^53 + 100 * q^55 - 20 * q^57 + 164 * q^59 - 124 * q^61 - 52 * q^63 + 52 * q^65 - 118 * q^67 + 72 * q^69 + 86 * q^71 + 58 * q^73 - 48 * q^75 + 40 * q^79 - 2 * q^81 + 188 * q^83 + 96 * q^85 - 38 * q^87 - 110 * q^89 - 52 * q^91 - 20 * q^93 + 78 * q^95 + 178 * q^97 - 208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.36603	−	2.36603i	0.455342	−	0.788675i	−0.543366	−	0.839496i	$-0.682850\pi$
$3$	1.36603	−	2.36603i	0.455342	−	0.788675i	0.998708	+	0.0508208i	$0.0161837\pi$
$4$		0			0
$5$	−4.36603	+	4.36603i	−0.873205	+	0.873205i	−0.992820	−	0.119615i	$-0.961834\pi$
$5$	−4.36603	+	4.36603i	−0.873205	+	0.873205i	0.119615	+	0.992820i	$0.461834\pi$
$6$		0			0
$7$	−2.26795	+	8.46410i	−0.323993	+	1.20916i	0.591328	+	0.806431i	$0.298604\pi$
$7$	−2.26795	+	8.46410i	−0.323993	+	1.20916i	−0.915321	+	0.402726i	$0.868063\pi$
$8$		0			0
$9$	0.767949	+	1.33013i	0.0853277	+	0.147792i
$10$		0			0
$11$	−6.19615	+	1.66025i	−0.563287	+	0.150932i	−0.529216	−	0.848487i	$-0.677514\pi$
$11$	−6.19615	+	1.66025i	−0.563287	+	0.150932i	−0.0340707	+	0.999419i	$0.510847\pi$
$12$		0			0
$13$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$13$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$14$		0			0
$15$	4.36603	+	16.2942i	0.291068	+	1.08628i
$16$		0			0
$17$	9.99038	−	5.76795i	0.587669	−	0.339291i	−0.176506	−	0.984300i	$-0.556479\pi$
$17$	9.99038	−	5.76795i	0.587669	−	0.339291i	0.764175	+	0.645008i	$0.223146\pi$
$18$		0			0
$19$	−3.36603	−	0.901924i	−0.177159	−	0.0474697i	0.169149	−	0.985591i	$-0.445898\pi$
$19$	−3.36603	−	0.901924i	−0.177159	−	0.0474697i	−0.346308	+	0.938121i	$0.612565\pi$
$20$		0			0
$21$	16.9282	+	16.9282i	0.806105	+	0.806105i
$22$		0			0
$23$	8.49038	+	4.90192i	0.369147	+	0.213127i	0.673086	−	0.739564i	$-0.264968\pi$
$23$	8.49038	+	4.90192i	0.369147	+	0.213127i	−0.303939	+	0.952692i	$0.598302\pi$
$24$		0			0
$25$		−	13.1244i		−	0.524974i
$26$		0			0
$27$	28.7846			1.06610
$28$		0			0
$29$	5.69615	−	9.86603i	0.196419	−	0.340208i	−0.750946	−	0.660364i	$-0.770402\pi$
$29$	5.69615	−	9.86603i	0.196419	−	0.340208i	0.947365	+	0.320156i	$0.103735\pi$
$30$		0			0
$31$	−1.92820	+	1.92820i	−0.0622001	+	0.0622001i	−0.737523	−	0.675322i	$-0.764004\pi$
$31$	−1.92820	+	1.92820i	−0.0622001	+	0.0622001i	0.675322	+	0.737523i	$0.264004\pi$
$32$		0			0
$33$	−4.53590	+	16.9282i	−0.137451	+	0.512976i
$34$		0			0
$35$	−27.0526	−	46.8564i	−0.772930	−	1.33875i
$36$		0			0
$37$	−42.1147	+	11.2846i	−1.13824	+	0.304989i	−0.778242	−	0.627965i	$-0.783888\pi$
$37$	−42.1147	+	11.2846i	−1.13824	+	0.304989i	−0.359995	+	0.932954i	$0.617221\pi$
$38$		0			0
$39$	17.7583	+	30.7583i	0.455342	+	0.788675i
$40$		0			0
$41$	5.08142	+	18.9641i	0.123937	+	0.462539i	0.999800	−	0.0200215i	$-0.00637348\pi$
$41$	5.08142	+	18.9641i	0.123937	+	0.462539i	−0.875863	+	0.482561i	$0.839707\pi$
$42$		0			0
$43$	−45.0000	+	25.9808i	−1.04651	+	0.604204i	−0.921671	−	0.387973i	$-0.873175\pi$
$43$	−45.0000	+	25.9808i	−1.04651	+	0.604204i	−0.124841	+	0.992177i	$0.539842\pi$
$44$		0			0
$45$	−9.16025	−	2.45448i	−0.203561	−	0.0545441i
$46$		0			0
$47$	−0.320508	−	0.320508i	−0.00681932	−	0.00681932i	0.703689	−	0.710508i	$-0.251535\pi$
$47$	−0.320508	−	0.320508i	−0.00681932	−	0.00681932i	−0.710508	+	0.703689i	$0.751535\pi$
$48$		0			0
$49$	−24.0622	−	13.8923i	−0.491065	−	0.283516i
$50$		0			0
$51$		−	31.5167i		−	0.617974i
$52$		0			0
$53$	78.7654			1.48614			0.743070	−	0.669214i	$-0.233369\pi$
$53$	78.7654			1.48614			0.743070	+	0.669214i	$0.233369\pi$
$54$		0			0
$55$	19.8038	−	34.3013i	0.360070	−	0.623659i
$56$		0			0
$57$	−6.73205	+	6.73205i	−0.118106	+	0.118106i
$58$		0			0
$59$	−10.9615	+	40.9090i	−0.185789	+	0.693372i	0.808672	+	0.588260i	$0.200187\pi$
$59$	−10.9615	+	40.9090i	−0.185789	+	0.693372i	−0.994460	+	0.105112i	$0.966480\pi$
$60$		0			0
$61$	−49.1865	−	85.1936i	−0.806337	−	1.39662i	−0.915385	−	0.402580i	$-0.868114\pi$
$61$	−49.1865	−	85.1936i	−0.806337	−	1.39662i	0.109048	−	0.994036i	$-0.465220\pi$
$62$		0			0
$63$	−13.0000	+	3.48334i	−0.206349	+	0.0552911i
$64$		0			0
$65$	−20.7750	−	77.5333i	−0.319615	−	1.19282i
$66$		0			0
$67$	−19.9737	−	74.5429i	−0.298115	−	1.11258i	−0.938712	−	0.344703i	$-0.887979\pi$
$67$	−19.9737	−	74.5429i	−0.298115	−	1.11258i	0.640596	−	0.767878i	$-0.278687\pi$
$68$		0			0
$69$	23.1962	−	13.3923i	0.336176	−	0.194091i
$70$		0			0
$71$	31.0263	+	8.31347i	0.436990	+	0.117091i	0.470605	−	0.882344i	$-0.344036\pi$
$71$	31.0263	+	8.31347i	0.436990	+	0.117091i	−0.0336156	+	0.999435i	$0.510702\pi$
$72$		0			0
$73$	48.2750	+	48.2750i	0.661301	+	0.661301i	0.955687	−	0.294386i	$-0.0951150\pi$
$73$	48.2750	+	48.2750i	0.661301	+	0.661301i	−0.294386	+	0.955687i	$0.595115\pi$
$74$		0			0
$75$	−31.0526	−	17.9282i	−0.414034	−	0.239043i
$76$		0			0
$77$		−	56.2102i		−	0.730003i
$78$		0			0
$79$	82.7461			1.04742			0.523710	−	0.851897i	$-0.324548\pi$
$79$	82.7461			1.04742			0.523710	+	0.851897i	$0.324548\pi$
$80$		0			0
$81$	32.4090	−	56.1340i	0.400111	−	0.693012i
$82$		0			0
$83$	69.5167	−	69.5167i	0.837550	−	0.837550i	−0.150986	−	0.988536i	$-0.548245\pi$
$83$	69.5167	−	69.5167i	0.837550	−	0.837550i	0.988536	+	0.150986i	$0.0482448\pi$
$84$		0			0
$85$	−18.4352	+	68.8013i	−0.216885	+	0.809427i
$86$		0			0
$87$	−15.5622	−	26.9545i	−0.178876	−	0.309822i
$88$		0			0
$89$	−31.8301	+	8.52886i	−0.357642	+	0.0958299i	−0.433166	−	0.901314i	$-0.642604\pi$
$89$	−31.8301	+	8.52886i	−0.357642	+	0.0958299i	0.0755242	+	0.997144i	$0.475937\pi$
$90$		0			0
$91$	−80.5500	−	80.5500i	−0.885165	−	0.885165i
$92$		0			0
$93$	1.92820	+	7.19615i	0.0207334	+	0.0773780i
$94$		0			0
$95$	18.6340	−	10.7583i	0.196147	−	0.113246i
$96$		0			0
$97$	74.8109	+	20.0455i	0.771246	+	0.206655i	0.622922	−	0.782284i	$-0.285945\pi$
$97$	74.8109	+	20.0455i	0.771246	+	0.206655i	0.148324	+	0.988939i	$0.452612\pi$
$98$		0			0
$99$	−6.96668	−	6.96668i	−0.0703705	−	0.0703705i
$100$		0			0
$101$	29.4404	+	16.9974i	0.291489	+	0.168291i	0.638613	−	0.769528i	$-0.279508\pi$
$101$	29.4404	+	16.9974i	0.291489	+	0.168291i	−0.347124	+	0.937819i	$0.612842\pi$
$102$		0			0
$103$			179.229i			1.74009i	0.492971	+	0.870046i	$0.335911\pi$
$103$			179.229i			1.74009i	−0.492971	+	0.870046i	$0.664089\pi$
$104$		0			0
$105$	−147.818			−1.40779
$106$		0			0
$107$	40.6673	−	70.4378i	0.380068	−	0.658297i	−0.611003	−	0.791628i	$-0.709234\pi$
$107$	40.6673	−	70.4378i	0.380068	−	0.658297i	0.991072	+	0.133331i	$0.0425672\pi$
$108$		0			0
$109$	−0.0192379	+	0.0192379i	−0.000176494	+	0.000176494i	−0.707195	−	0.707019i	$-0.750040\pi$
$109$	−0.0192379	+	0.0192379i	−0.000176494	+	0.000176494i	0.707019	+	0.707195i	$0.250040\pi$
$110$		0			0
$111$	−30.8301	+	115.060i	−0.277749	+	1.03657i
$112$		0			0
$113$	46.0096	+	79.6910i	0.407165	+	0.705230i	0.994571	−	0.104062i	$-0.0331841\pi$
$113$	46.0096	+	79.6910i	0.407165	+	0.705230i	−0.587406	+	0.809292i	$0.699851\pi$
$114$		0			0
$115$	−58.4711	+	15.6673i	−0.508445	+	0.136237i
$116$		0			0
$117$	−19.9667			−0.170655
$118$		0			0
$119$	26.1628	+	97.6410i	0.219856	+	0.820513i
$120$		0			0
$121$	−69.1532	+	39.9256i	−0.571514	+	0.329964i
$122$		0			0
$123$	51.8109	+	13.8827i	0.421227	+	0.112867i
$124$		0			0
$125$	−51.8494	−	51.8494i	−0.414795	−	0.414795i
$126$		0			0
$127$	−63.6673	−	36.7583i	−0.501317	−	0.289436i	0.227940	−	0.973675i	$-0.426801\pi$
$127$	−63.6673	−	36.7583i	−0.501317	−	0.289436i	−0.729257	+	0.684239i	$0.760134\pi$
$128$		0			0
$129$			141.962i			1.10048i
$130$		0			0
$131$	−48.9808			−0.373899			−0.186949	−	0.982370i	$-0.559860\pi$
$131$	−48.9808			−0.373899			−0.186949	+	0.982370i	$0.559860\pi$
$132$		0			0
$133$	15.2679	−	26.4449i	0.114797	−	0.198834i
$134$		0			0
$135$	−125.674	+	125.674i	−0.930921	+	0.930921i
$136$		0			0
$137$	18.3949	−	68.6506i	0.134269	−	0.501100i	−0.865731	−	0.500510i	$-0.833146\pi$
$137$	18.3949	−	68.6506i	0.134269	−	0.501100i	1.00000		0.000589281i	$-0.000187574\pi$
$138$		0			0
$139$	57.7846	+	100.086i	0.415717	+	0.720042i	0.995503	−	0.0947259i	$-0.0301975\pi$
$139$	57.7846	+	100.086i	0.415717	+	0.720042i	−0.579787	+	0.814768i	$0.696864\pi$
$140$		0			0
$141$	−1.19615	+	0.320508i	−0.00848335	+	0.00227311i
$142$		0			0
$143$	21.5833	−	80.5500i	0.150932	−	0.563287i
$144$		0			0
$145$	18.2058	+	67.9449i	0.125557	+	0.468585i
$146$		0			0
$147$	−65.7391	+	37.9545i	−0.447205	+	0.258194i
$148$		0			0
$149$	263.090	+	70.4948i	1.76571	+	0.473120i	0.987862	−	0.155336i	$-0.0496460\pi$
$149$	263.090	+	70.4948i	1.76571	+	0.473120i	0.777845	+	0.628456i	$0.216313\pi$
$150$		0			0
$151$	65.9948	+	65.9948i	0.437052	+	0.437052i	0.891019	−	0.453967i	$-0.149991\pi$
$151$	65.9948	+	65.9948i	0.437052	+	0.437052i	−0.453967	+	0.891019i	$0.649991\pi$
$152$		0			0
$153$	15.3442	+	8.85898i	0.100289	+	0.0579019i
$154$		0			0
$155$		−	16.8372i		−	0.108627i
$156$		0			0
$157$	47.7461			0.304116			0.152058	−	0.988372i	$-0.451410\pi$
$157$	47.7461			0.304116			0.152058	+	0.988372i	$0.451410\pi$
$158$		0			0
$159$	107.595	−	186.361i	0.676701	−	1.17208i
$160$		0			0
$161$	−60.7461	+	60.7461i	−0.377305	+	0.377305i
$162$		0			0
$163$	−16.2820	+	60.7654i	−0.0998898	+	0.372794i	−0.997715	−	0.0675575i	$-0.978479\pi$
$163$	−16.2820	+	60.7654i	−0.0998898	+	0.372794i	0.897826	+	0.440351i	$0.145146\pi$
$164$		0			0
$165$	−54.1051	−	93.7128i	−0.327910	−	0.567956i
$166$		0			0
$167$	176.406	−	47.2679i	1.05633	−	0.283042i	0.311462	−	0.950259i	$-0.399181\pi$
$167$	176.406	−	47.2679i	1.05633	−	0.283042i	0.744863	+	0.667217i	$0.232515\pi$
$168$		0			0
$169$	−84.5000	−	146.358i	−0.500000	−	0.866025i
$170$		0			0
$171$	−1.38526	−	5.16987i	−0.00810095	−	0.0302332i
$172$		0			0
$173$	−244.865	+	141.373i	−1.41541	+	0.817185i	−0.995891	−	0.0905627i	$-0.971133\pi$
$173$	−244.865	+	141.373i	−1.41541	+	0.817185i	−0.419516	+	0.907748i	$0.637800\pi$
$174$		0			0
$175$	111.086	+	29.7654i	0.634776	+	0.170088i
$176$		0			0
$177$	81.8179	+	81.8179i	0.462248	+	0.462248i
$178$		0			0
$179$	258.904	+	149.478i	1.44639	+	0.835074i	0.998264	−	0.0588968i	$-0.0187583\pi$
$179$	258.904	+	149.478i	1.44639	+	0.835074i	0.448126	+	0.893970i	$0.352092\pi$
$180$		0			0
$181$			299.081i			1.65238i	0.563392	+	0.826190i	$0.309496\pi$
$181$			299.081i			1.65238i	−0.563392	+	0.826190i	$0.690504\pi$
$182$		0			0
$183$	−268.760			−1.46864
$184$		0			0
$185$	134.605	−	233.143i	0.727595	−	1.26023i
$186$		0			0
$187$	−52.3257	+	52.3257i	−0.279816	+	0.279816i
$188$		0			0
$189$	−65.2820	+	243.636i	−0.345408	+	1.28908i
$190$		0			0
$191$	−118.002	−	204.385i	−0.617811	−	1.07008i	−0.989884	−	0.141877i	$-0.954686\pi$
$191$	−118.002	−	204.385i	−0.617811	−	1.07008i	0.372073	−	0.928203i	$-0.378647\pi$
$192$		0			0
$193$	312.449	−	83.7205i	1.61891	−	0.433785i	0.668228	−	0.743957i	$-0.267053\pi$
$193$	312.449	−	83.7205i	1.61891	−	0.433785i	0.950681	+	0.310172i	$0.100386\pi$
$194$		0			0
$195$	−211.825	−	56.7583i	−1.08628	−	0.291068i
$196$		0			0
$197$	−62.1122	−	231.806i	−0.315290	−	1.17668i	−0.923719	−	0.383071i	$-0.874867\pi$
$197$	−62.1122	−	231.806i	−0.315290	−	1.17668i	0.608429	−	0.793608i	$-0.291800\pi$
$198$		0			0
$199$	−44.5481	+	25.7199i	−0.223860	+	0.129245i	−0.607736	−	0.794139i	$-0.707922\pi$
$199$	−44.5481	+	25.7199i	−0.223860	+	0.129245i	0.383876	+	0.923384i	$0.374589\pi$
$200$		0			0
$201$	−203.655	−	54.5692i	−1.01321	−	0.271489i
$202$		0			0
$203$	70.5885	+	70.5885i	0.347726	+	0.347726i
$204$		0			0
$205$	−104.983	−	60.6122i	−0.512114	−	0.295669i
$206$		0			0
$207$			15.0577i			0.0727426i
$208$		0			0
$209$	22.3538			0.106956
$210$		0			0
$211$	−103.648	+	179.524i	−0.491223	+	0.850823i	−0.999949	−	0.0101053i	$-0.996783\pi$
$211$	−103.648	+	179.524i	−0.491223	+	0.850823i	0.508726	+	0.860929i	$0.330117\pi$
$212$		0			0
$213$	62.0526	−	62.0526i	0.291327	−	0.291327i
$214$		0			0
$215$	83.0385	−	309.904i	0.386225	−	1.44141i
$216$		0			0
$217$	−11.9474	−	20.6936i	−0.0550573	−	0.0953621i
$218$		0			0
$219$	180.165	−	48.2750i	0.822670	−	0.220434i
$220$		0			0
$221$			149.967i			0.678582i
$222$		0			0
$223$	−84.5326	−	315.480i	−0.379070	−	1.41471i	−0.847306	−	0.531105i	$-0.821777\pi$
$223$	−84.5326	−	315.480i	−0.379070	−	1.41471i	0.468236	−	0.883604i	$-0.344890\pi$
$224$		0			0
$225$	17.4571	−	10.0788i	0.0775869	−	0.0447948i
$226$		0			0
$227$	234.720	+	62.8930i	1.03401	+	0.277062i	0.735628	−	0.677386i	$-0.236887\pi$
$227$	234.720	+	62.8930i	1.03401	+	0.277062i	0.298380	+	0.954447i	$0.403554\pi$
$228$		0			0
$229$	−75.7321	−	75.7321i	−0.330708	−	0.330708i	0.522148	−	0.852855i	$-0.325131\pi$
$229$	−75.7321	−	75.7321i	−0.330708	−	0.330708i	−0.852855	+	0.522148i	$0.825131\pi$
$230$		0			0
$231$	−132.995	−	76.7846i	−0.575735	−	0.332401i
$232$		0			0
$233$		−	304.592i		−	1.30726i	−0.756813	−	0.653631i	$-0.773245\pi$
$233$		−	304.592i		−	1.30726i	0.756813	−	0.653631i	$-0.226755\pi$
$234$		0			0
$235$	2.79869			0.0119093
$236$		0			0
$237$	113.033	−	195.779i	0.476934	−	0.826074i
$238$		0			0
$239$	−250.655	+	250.655i	−1.04877	+	1.04877i	−0.0500178	+	0.998748i	$0.515928\pi$
$239$	−250.655	+	250.655i	−1.04877	+	1.04877i	−0.998748	+	0.0500178i	$0.984072\pi$
$240$		0			0
$241$	11.6487	−	43.4737i	0.0483351	−	0.180389i	−0.937538	−	0.347883i	$-0.886901\pi$
$241$	11.6487	−	43.4737i	0.0483351	−	0.180389i	0.985873	+	0.167494i	$0.0535674\pi$
$242$		0			0
$243$	40.9878	+	70.9930i	0.168674	+	0.292152i
$244$		0			0
$245$	165.710	−	44.4019i	0.676368	−	0.181232i
$246$		0			0
$247$	32.0333	−	32.0333i	0.129690	−	0.129690i
$248$		0			0
$249$	−69.5167	−	259.440i	−0.279183	−	1.04193i
$250$		0			0
$251$	−116.375	+	67.1891i	−0.463645	+	0.267686i	−0.713576	−	0.700578i	$-0.752926\pi$
$251$	−116.375	+	67.1891i	−0.463645	+	0.267686i	0.249931	+	0.968264i	$0.419592\pi$
$252$		0			0
$253$	−60.7461	−	16.2769i	−0.240103	−	0.0643355i
$254$		0			0
$255$	137.603	+	137.603i	0.539618	+	0.539618i
$256$		0			0
$257$	283.227	+	163.521i	1.10205	+	0.636269i	0.936759	−	0.349976i	$-0.113810\pi$
$257$	283.227	+	163.521i	1.10205	+	0.636269i	0.165291	+	0.986245i	$0.447144\pi$
$258$		0			0
$259$		−	382.056i		−	1.47512i
$260$		0			0
$261$	17.4974			0.0670399
$262$		0			0
$263$	225.669	−	390.870i	0.858058	−	1.48620i	−0.0157213	−	0.999876i	$-0.505004\pi$
$263$	225.669	−	390.870i	0.858058	−	1.48620i	0.873779	−	0.486323i	$-0.161662\pi$
$264$		0			0
$265$	−343.892	+	343.892i	−1.29770	+	1.29770i
$266$		0			0
$267$	−23.3013	+	86.9615i	−0.0872707	+	0.325699i
$268$		0			0
$269$	−78.3538	−	135.713i	−0.291278	−	0.504509i	0.682834	−	0.730573i	$-0.260747\pi$
$269$	−78.3538	−	135.713i	−0.291278	−	0.504509i	−0.974112	+	0.226065i	$0.927414\pi$
$270$		0			0
$271$	−247.133	+	66.2192i	−0.911931	+	0.244351i	−0.684133	−	0.729357i	$-0.739819\pi$
$271$	−247.133	+	66.2192i	−0.911931	+	0.244351i	−0.227798	+	0.973708i	$0.573153\pi$
$272$		0			0
$273$	−300.617	+	80.5500i	−1.10116	+	0.295055i
$274$		0			0
$275$	21.7898	+	81.3205i	0.0792355	+	0.295711i
$276$		0			0
$277$	−57.8904	+	33.4230i	−0.208991	+	0.120661i	−0.600842	−	0.799368i	$-0.705168\pi$
$277$	−57.8904	+	33.4230i	−0.208991	+	0.120661i	0.391852	+	0.920028i	$0.371835\pi$
$278$		0			0
$279$	−4.04552	−	1.08399i	−0.0145001	−	0.00388528i
$280$		0			0
$281$	111.026	+	111.026i	0.395111	+	0.395111i	0.876505	−	0.481393i	$-0.159869\pi$
$281$	111.026	+	111.026i	0.395111	+	0.395111i	−0.481393	+	0.876505i	$0.659869\pi$
$282$		0			0
$283$	41.1962	+	23.7846i	0.145569	+	0.0840446i	0.571016	−	0.820939i	$-0.306550\pi$
$283$	41.1962	+	23.7846i	0.145569	+	0.0840446i	−0.425446	+	0.904984i	$0.639883\pi$
$284$		0			0
$285$		−	58.7846i		−	0.206262i
$286$		0			0
$287$	−172.038			−0.599437
$288$		0			0
$289$	−77.9615	+	135.033i	−0.269763	+	0.467243i
$290$		0			0
$291$	149.622	−	149.622i	0.514164	−	0.514164i
$292$		0			0
$293$	2.24236	−	8.36860i	0.00765311	−	0.0285618i	−0.961994	−	0.273072i	$-0.911960\pi$
$293$	2.24236	−	8.36860i	0.00765311	−	0.0285618i	0.969647	+	0.244510i	$0.0786271\pi$
$294$		0			0
$295$	−130.751	−	226.468i	−0.443225	−	0.767688i
$296$		0			0
$297$	−178.354	+	47.7898i	−0.600518	+	0.160908i
$298$		0			0
$299$	−110.375	+	63.7250i	−0.369147	+	0.213127i
$300$		0			0
$301$	−117.846	−	439.808i	−0.391515	−	1.46115i
$302$		0			0
$303$	80.4327	−	46.4378i	0.265454	−	0.153260i
$304$		0			0
$305$	586.707	+	157.208i	1.92363	+	0.515435i
$306$		0			0
$307$	228.219	+	228.219i	0.743385	+	0.743385i	0.973228	−	0.229843i	$-0.0738212\pi$
$307$	228.219	+	228.219i	0.743385	+	0.743385i	−0.229843	+	0.973228i	$0.573821\pi$
$308$		0			0
$309$	424.061	+	244.832i	1.37237	+	0.792337i
$310$		0			0
$311$		−	77.4782i		−	0.249126i	−0.992212	−	0.124563i	$-0.960247\pi$
$311$		−	77.4782i		−	0.249126i	0.992212	−	0.124563i	$-0.0397529\pi$
$312$		0			0
$313$	−165.685			−0.529344			−0.264672	−	0.964339i	$-0.585264\pi$
$313$	−165.685			−0.529344			−0.264672	+	0.964339i	$0.585264\pi$
$314$		0			0
$315$	41.5500	−	71.9667i	0.131905	−	0.228466i
$316$		0			0
$317$	97.0544	−	97.0544i	0.306165	−	0.306165i	−0.537255	−	0.843420i	$-0.680539\pi$
$317$	97.0544	−	97.0544i	0.306165	−	0.306165i	0.843420	+	0.537255i	$0.180539\pi$
$318$		0			0
$319$	−18.9141	+	70.5885i	−0.0592919	+	0.221280i
$320$		0			0
$321$	−111.105	−	192.440i	−0.346122	−	0.599501i
$322$		0			0
$323$	−38.8301	+	10.4045i	−0.120217	+	0.0322121i
$324$		0			0
$325$	147.758	+	85.3083i	0.454641	+	0.262487i
$326$		0			0
$327$	0.0192379	+	0.0717968i	5.88315e−5	+	0.000219562i
$328$		0			0
$329$	3.43971	−	1.98592i	0.0104550	−	0.00603622i
$330$		0			0
$331$	292.603	+	78.4026i	0.883996	+	0.236866i	0.672130	−	0.740433i	$-0.265379\pi$
$331$	292.603	+	78.4026i	0.883996	+	0.236866i	0.211865	+	0.977299i	$0.432046\pi$
$332$		0			0
$333$	−47.3519	−	47.3519i	−0.142198	−	0.142198i
$334$		0			0
$335$	412.662	+	238.251i	1.23183	+	0.711196i
$336$		0			0
$337$		−	90.7795i		−	0.269375i	−0.990888	−	0.134688i	$-0.956997\pi$
$337$		−	90.7795i		−	0.269375i	0.990888	−	0.134688i	$-0.0430031\pi$
$338$		0			0
$339$	251.401			0.741597
$340$		0			0
$341$	8.74613	−	15.1487i	0.0256485	−	0.0444245i
$342$		0			0
$343$	−131.454	+	131.454i	−0.383247	+	0.383247i
$344$		0			0
$345$	−42.8038	+	159.746i	−0.124069	+	0.463032i
$346$		0			0
$347$	−52.5903	−	91.0891i	−0.151557	−	0.262505i	0.780243	−	0.625477i	$-0.215095\pi$
$347$	−52.5903	−	91.0891i	−0.151557	−	0.262505i	−0.931800	+	0.362972i	$0.881762\pi$
$348$		0			0
$349$	158.040	−	42.3468i	0.452838	−	0.121338i	−0.0251892	−	0.999683i	$-0.508019\pi$
$349$	158.040	−	42.3468i	0.452838	−	0.121338i	0.478027	+	0.878345i	$0.341352\pi$
$350$		0			0
$351$	−187.100	+	324.067i	−0.533048	+	0.923267i
$352$		0			0
$353$	77.1692	+	287.999i	0.218610	+	0.815862i	0.984865	+	0.173325i	$0.0554513\pi$
$353$	77.1692	+	287.999i	0.218610	+	0.815862i	−0.766255	+	0.642537i	$0.777882\pi$
$354$		0			0
$355$	−171.758	+	99.1647i	−0.483826	+	0.279337i
$356$		0			0
$357$	266.760	+	71.4782i	0.747227	+	0.200219i
$358$		0			0
$359$	−299.923	−	299.923i	−0.835440	−	0.835440i	0.152815	−	0.988255i	$-0.451166\pi$
$359$	−299.923	−	299.923i	−0.835440	−	0.835440i	−0.988255	+	0.152815i	$0.951166\pi$
$360$		0			0
$361$	−302.119	−	174.428i	−0.836893	−	0.483181i
$362$		0			0
$363$			218.158i			0.600985i
$364$		0			0
$365$	−421.540			−1.15490
$366$		0			0
$367$	−61.2750	+	106.131i	−0.166962	+	0.289186i	−0.937350	−	0.348388i	$-0.886729\pi$
$367$	−61.2750	+	106.131i	−0.166962	+	0.289186i	0.770388	+	0.637575i	$0.220062\pi$
$368$		0			0
$369$	−21.3224	+	21.3224i	−0.0577843	+	0.0577843i
$370$		0			0
$371$	−178.636	+	666.678i	−0.481498	+	1.79698i
$372$		0			0
$373$	−10.6384	−	18.4263i	−0.0285213	−	0.0494003i	0.851412	−	0.524497i	$-0.175747\pi$
$373$	−10.6384	−	18.4263i	−0.0285213	−	0.0494003i	−0.879934	+	0.475096i	$0.842413\pi$
$374$		0			0
$375$	−193.504	+	51.8494i	−0.516012	+	0.138265i
$376$		0			0
$377$	74.0500	+	128.258i	0.196419	+	0.340208i
$378$		0			0
$379$	−87.1417	−	325.217i	−0.229925	−	0.858093i	−0.980371	−	0.197161i	$-0.936828\pi$
$379$	−87.1417	−	325.217i	−0.229925	−	0.858093i	0.750446	−	0.660932i	$-0.229839\pi$
$380$		0			0
$381$	−173.942	+	100.426i	−0.456541	+	0.263584i
$382$		0			0
$383$	183.061	+	49.0512i	0.477967	+	0.128071i	0.489756	−	0.871860i	$-0.337086\pi$
$383$	183.061	+	49.0512i	0.477967	+	0.128071i	−0.0117887	+	0.999931i	$0.503753\pi$
$384$		0			0
$385$	245.415	+	245.415i	0.637442	+	0.637442i
$386$		0			0
$387$	−69.1154	−	39.9038i	−0.178593	−	0.103111i
$388$		0			0
$389$			195.522i			0.502627i	0.967906	+	0.251313i	$0.0808625\pi$
$389$			195.522i			0.502627i	−0.967906	+	0.251313i	$0.919138\pi$
$390$		0			0
$391$	113.096			0.289249
$392$		0			0
$393$	−66.9090	+	115.890i	−0.170252	+	0.294885i
$394$		0			0
$395$	−361.272	+	361.272i	−0.914612	+	0.914612i
$396$		0			0
$397$	−108.578	+	405.217i	−0.273495	+	1.02070i	0.683348	+	0.730093i	$0.260523\pi$
$397$	−108.578	+	405.217i	−0.273495	+	1.02070i	−0.956843	+	0.290605i	$0.906143\pi$
$398$		0			0
$399$	−41.7128	−	72.2487i	−0.104543	−	0.181074i
$400$		0			0
$401$	−753.833	+	201.989i	−1.87988	+	0.503713i	−0.880313	+	0.474393i	$0.842668\pi$
$401$	−753.833	+	201.989i	−1.87988	+	0.503713i	−0.999570	+	0.0293204i	$0.990666\pi$
$402$		0			0
$403$	−9.17503	−	34.2417i	−0.0227668	−	0.0849669i
$404$		0			0
$405$	103.584	+	386.581i	0.255763	+	0.954520i
$406$		0			0
$407$	242.214	−	139.842i	0.595120	−	0.343593i
$408$		0			0
$409$	353.679	+	94.7679i	0.864740	+	0.231706i	0.663812	−	0.747899i	$-0.268937\pi$
$409$	353.679	+	94.7679i	0.864740	+	0.231706i	0.200928	+	0.979606i	$0.435604\pi$
$410$		0			0
$411$	−137.301	−	137.301i	−0.334066	−	0.334066i
$412$		0			0
$413$	−321.397	−	185.559i	−0.778202	−	0.449295i
$414$		0			0
$415$			607.023i			1.46271i
$416$		0			0
$417$	315.741			0.757173
$418$		0			0
$419$	−275.279	+	476.797i	−0.656990	+	1.13794i	0.324401	+	0.945920i	$0.394837\pi$
$419$	−275.279	+	476.797i	−0.656990	+	1.13794i	−0.981391	+	0.192020i	$0.938496\pi$
$420$		0			0
$421$	−233.619	+	233.619i	−0.554913	+	0.554913i	−0.927855	−	0.372942i	$-0.878349\pi$
$421$	−233.619	+	233.619i	−0.554913	+	0.554913i	0.372942	+	0.927855i	$0.378349\pi$
$422$		0			0
$423$	0.180183	−	0.672450i	0.000425963	−	0.00158972i
$424$		0			0
$425$	−75.7006	−	131.117i	−0.178119	−	0.308511i
$426$		0			0
$427$	832.640	−	223.105i	1.94998	−	0.522494i
$428$		0			0
$429$	−161.100	−	161.100i	−0.375524	−	0.375524i
$430$		0			0
$431$	−188.301	−	702.750i	−0.436894	−	1.63051i	−0.736493	−	0.676445i	$-0.763520\pi$
$431$	−188.301	−	702.750i	−0.436894	−	1.63051i	0.299599	−	0.954065i	$-0.403147\pi$
$432$		0			0
$433$	576.108	−	332.616i	1.33050	−	0.768166i	0.345126	−	0.938556i	$-0.387836\pi$
$433$	576.108	−	332.616i	1.33050	−	0.768166i	0.985377	+	0.170390i	$0.0545028\pi$
$434$		0			0
$435$	185.629	+	49.7391i	0.426733	+	0.114343i
$436$		0			0
$437$	−24.1577	−	24.1577i	−0.0552807	−	0.0552807i
$438$		0			0
$439$	−233.942	−	135.067i	−0.532898	−	0.307669i	0.209298	−	0.977852i	$-0.432882\pi$
$439$	−233.942	−	135.067i	−0.532898	−	0.307669i	−0.742196	+	0.670183i	$0.766216\pi$
$440$		0			0
$441$		−	42.6743i		−	0.0967672i
$442$		0			0
$443$	−309.723			−0.699149			−0.349575	−	0.936909i	$-0.613674\pi$
$443$	−309.723			−0.699149			−0.349575	+	0.936909i	$0.613674\pi$
$444$		0			0
$445$	101.734	−	176.208i	0.228616	−	0.395974i
$446$		0			0
$447$	526.181	−	526.181i	1.17714	−	1.17714i
$448$		0			0
$449$	114.399	−	426.944i	0.254787	−	0.950878i	−0.713422	−	0.700735i	$-0.752856\pi$
$449$	114.399	−	426.944i	0.254787	−	0.950878i	0.968209	−	0.250143i	$-0.0804777\pi$
$450$		0			0
$451$	−62.9705	−	109.068i	−0.139624	−	0.241836i
$452$		0			0
$453$	246.296	−	65.9948i	0.543700	−	0.145684i
$454$		0			0
$455$	703.367			1.54586
$456$		0			0
$457$	−46.6980	−	174.279i	−0.102184	−	0.381355i	0.895827	−	0.444404i	$-0.146584\pi$
$457$	−46.6980	−	174.279i	−0.102184	−	0.381355i	−0.998010	+	0.0630483i	$0.979918\pi$
$458$		0			0
$459$	287.569	−	166.028i	0.626512	−	0.361717i
$460$		0			0
$461$	−201.397	−	53.9641i	−0.436869	−	0.117059i	0.0336796	−	0.999433i	$-0.489277\pi$
$461$	−201.397	−	53.9641i	−0.436869	−	0.117059i	−0.470549	+	0.882374i	$0.655944\pi$
$462$		0			0
$463$	316.809	+	316.809i	0.684253	+	0.684253i	0.960956	−	0.276703i	$-0.0892418\pi$
$463$	316.809	+	316.809i	0.684253	+	0.684253i	−0.276703	+	0.960956i	$0.589242\pi$
$464$		0			0
$465$	−39.8372	−	23.0000i	−0.0856713	−	0.0494624i
$466$		0			0
$467$		−	357.415i		−	0.765343i	−0.923884	−	0.382672i	$-0.875004\pi$
$467$		−	357.415i		−	0.765343i	0.923884	−	0.382672i	$-0.124996\pi$
$468$		0			0
$469$	676.238			1.44187
$470$		0			0
$471$	65.2224	−	112.969i	0.138477	−	0.239848i
$472$		0			0
$473$	235.692	−	235.692i	0.498292	−	0.498292i
$474$		0			0
$475$	−11.8372	+	44.1769i	−0.0249204	+	0.0930040i
$476$		0			0
$477$	60.4878	+	104.768i	0.126809	+	0.219639i
$478$		0			0
$479$	−417.217	+	111.793i	−0.871017	+	0.233388i	−0.666528	−	0.745480i	$-0.732220\pi$
$479$	−417.217	+	111.793i	−0.871017	+	0.233388i	−0.204490	+	0.978869i	$0.565553\pi$
$480$		0			0
$481$	146.700	−	547.492i	0.304989	−	1.13824i
$482$		0			0
$483$	60.7461	+	226.708i	0.125768	+	0.469374i
$484$		0			0
$485$	−414.145	+	239.107i	−0.853908	+	0.493004i
$486$		0			0
$487$	−286.937	−	76.8846i	−0.589193	−	0.157874i	−0.0481088	−	0.998842i	$-0.515319\pi$
$487$	−286.937	−	76.8846i	−0.589193	−	0.157874i	−0.541084	+	0.840968i	$0.681986\pi$
$488$		0			0
$489$	121.531	+	121.531i	0.248529	+	0.248529i
$490$		0			0
$491$	−685.319	−	395.669i	−1.39576	−	0.805844i	−0.401817	−	0.915720i	$-0.631621\pi$
$491$	−685.319	−	395.669i	−1.39576	−	0.805844i	−0.993945	+	0.109877i	$0.964954\pi$
$492$		0			0
$493$		−	131.420i		−	0.266573i
$494$		0			0
$495$	60.8334			0.122896
$496$		0			0
$497$	−140.732	+	243.755i	−0.283163	+	0.490453i
$498$		0			0
$499$	307.603	−	307.603i	0.616438	−	0.616438i	−0.328178	−	0.944616i	$-0.606435\pi$
$499$	307.603	−	307.603i	0.616438	−	0.616438i	0.944616	+	0.328178i	$0.106435\pi$
$500$		0			0
$501$	129.138	−	481.951i	0.257761	−	0.961978i
$502$		0			0
$503$	142.200	+	246.297i	0.282704	+	0.489657i	0.972050	−	0.234775i	$-0.0754354\pi$
$503$	142.200	+	246.297i	0.282704	+	0.489657i	−0.689346	+	0.724432i	$0.742102\pi$
$504$		0			0
$505$	−202.749	+	54.3264i	−0.401483	+	0.107577i
$506$		0			0
$507$	−461.717			−0.910684
$508$		0			0
$509$	3.39488	+	12.6699i	0.00666971	+	0.0248917i	0.969180	−	0.246352i	$-0.0792318\pi$
$509$	3.39488	+	12.6699i	0.00666971	+	0.0248917i	−0.962511	+	0.271243i	$0.912565\pi$
$510$		0			0
$511$	−518.090	+	299.119i	−1.01387	+	0.585360i
$512$		0			0
$513$	−96.8897	−	25.9615i	−0.188869	−	0.0506073i
$514$		0			0
$515$	−782.520	−	782.520i	−1.51946	−	1.51946i
$516$		0			0
$517$	2.51804	+	1.45379i	0.00487049	+	0.00281198i
$518$		0			0
$519$			772.477i			1.48839i
$520$		0			0
$521$	−913.011			−1.75242			−0.876210	−	0.481929i	$-0.839936\pi$
$521$	−913.011			−1.75242			−0.876210	+	0.481929i	$0.839936\pi$
$522$		0			0
$523$	375.827	−	650.951i	0.718598	−	1.24465i	−0.242957	−	0.970037i	$-0.578117\pi$
$523$	375.827	−	650.951i	0.718598	−	1.24465i	0.961555	−	0.274612i	$-0.0885493\pi$
$524$		0			0
$525$	222.172	−	222.172i	0.423184	−	0.423184i
$526$		0			0
$527$	−8.14171	+	30.3853i	−0.0154492	+	0.0576570i
$528$		0			0
$529$	−216.442	−	374.889i	−0.409154	−	0.708675i
$530$		0			0
$531$	−62.8320	+	16.8358i	−0.118328	+	0.0317058i
$532$		0			0
$533$	−246.533	−	66.0584i	−0.462539	−	0.123937i
$534$		0			0
$535$	129.979	+	485.088i	0.242951	+	0.906706i
$536$		0			0
$537$	707.338	−	408.382i	1.31720	−	0.760488i
$538$		0			0
$539$	172.158	+	46.1295i	0.319402	+	0.0855835i
$540$		0			0
$541$	125.371	+	125.371i	0.231740	+	0.231740i	0.813419	−	0.581679i	$-0.197604\pi$
$541$	125.371	+	125.371i	0.231740	+	0.231740i	−0.581679	+	0.813419i	$0.697604\pi$
$542$		0			0
$543$	707.633	+	408.552i	1.30319	+	0.752398i
$544$		0			0
$545$		−	0.167986i		−	0.000308232i
$546$		0			0
$547$	465.096			0.850267			0.425134	−	0.905131i	$-0.360227\pi$
$547$	465.096			0.850267			0.425134	+	0.905131i	$0.360227\pi$
$548$		0			0
$549$	75.5455	−	130.849i	0.137606	−	0.238340i
$550$		0			0
$551$	−28.0718	+	28.0718i	−0.0509470	+	0.0509470i
$552$		0			0
$553$	−187.664	+	700.372i	−0.339356	+	1.26649i
$554$		0			0
$555$	−367.748	−	636.958i	−0.662609	−	1.14767i
$556$		0			0
$557$	246.064	−	65.9327i	0.441767	−	0.118371i	−0.0310777	−	0.999517i	$-0.509894\pi$
$557$	246.064	−	65.9327i	0.441767	−	0.118371i	0.472844	+	0.881146i	$0.343227\pi$
$558$		0			0
$559$		−	675.500i		−	1.20841i
$560$		0			0
$561$	52.3257	+	195.282i	0.0932721	+	0.348096i
$562$		0			0
$563$	−306.888	+	177.182i	−0.545095	+	0.314711i	−0.747141	−	0.664665i	$-0.768574\pi$
$563$	−306.888	+	177.182i	−0.545095	+	0.314711i	0.202046	+	0.979376i	$0.435241\pi$
$564$		0			0
$565$	−548.812	−	147.054i	−0.971349	−	0.260272i
$566$		0			0
$567$	401.622	+	401.622i	0.708328	+	0.708328i
$568$		0			0
$569$	−152.685	−	88.1525i	−0.268339	−	0.154925i	0.359794	−	0.933032i	$-0.382847\pi$
$569$	−152.685	−	88.1525i	−0.268339	−	0.154925i	−0.628132	+	0.778106i	$0.716180\pi$
$570$		0			0
$571$		−	569.751i		−	0.997813i	−0.866656	−	0.498907i	$-0.833735\pi$
$571$		−	569.751i		−	0.997813i	0.866656	−	0.498907i	$-0.166265\pi$
$572$		0			0
$573$	−644.774			−1.12526
$574$		0			0
$575$	64.3346	−	111.431i	0.111886	−	0.193793i
$576$		0			0
$577$	−94.7635	+	94.7635i	−0.164235	+	0.164235i	−0.784440	−	0.620205i	$-0.787049\pi$
$577$	−94.7635	+	94.7635i	−0.164235	+	0.164235i	0.620205	+	0.784440i	$0.287049\pi$
$578$		0			0
$579$	228.729	−	853.627i	0.395041	−	1.47431i
$580$		0			0
$581$	430.736	+	746.056i	0.741370	+	1.28409i
$582$		0			0
$583$	−488.042	+	130.771i	−0.837122	+	0.224306i
$584$		0			0
$585$	87.1750	−	87.1750i	0.149017	−	0.149017i
$586$		0			0
$587$	283.123	+	1056.63i	0.482322	+	1.80005i	0.591829	+	0.806064i	$0.298406\pi$
$587$	283.123	+	1056.63i	0.482322	+	1.80005i	−0.109507	+	0.993986i	$0.534927\pi$
$588$		0			0
$589$	8.22947	−	4.75129i	0.0139719	−	0.00806670i
$590$		0			0
$591$	−633.305	−	169.694i	−1.07158	−	0.287130i
$592$		0			0
$593$	−228.671	−	228.671i	−0.385617	−	0.385617i	0.487504	−	0.873121i	$-0.337908\pi$
$593$	−228.671	−	228.671i	−0.385617	−	0.385617i	−0.873121	+	0.487504i	$0.837908\pi$
$594$		0			0
$595$	−540.531	−	312.076i	−0.908455	−	0.524497i
$596$		0			0
$597$			140.536i			0.235404i
$598$		0			0
$599$	282.596			0.471780			0.235890	−	0.971780i	$-0.424200\pi$
$599$	282.596			0.471780			0.235890	+	0.971780i	$0.424200\pi$
$600$		0			0
$601$	70.6558	−	122.379i	0.117564	−	0.203626i	−0.801238	−	0.598346i	$-0.795825\pi$
$601$	70.6558	−	122.379i	0.117564	−	0.203626i	0.918802	+	0.394720i	$0.129158\pi$
$602$		0			0
$603$	83.8128	−	83.8128i	0.138993	−	0.138993i
$604$		0			0
$605$	127.608	−	476.241i	0.210923	−	0.787175i
$606$		0			0
$607$	344.398	+	596.515i	0.567377	+	0.982726i	0.996824	+	0.0796341i	$0.0253752\pi$
$607$	344.398	+	596.515i	0.567377	+	0.982726i	−0.429447	+	0.903092i	$0.641291\pi$
$608$		0			0
$609$	263.440	−	70.5885i	0.432578	−	0.115909i
$610$		0			0
$611$	5.69169	−	1.52508i	0.00931537	−	0.00249604i
$612$		0			0
$613$	33.1608	+	123.758i	0.0540959	+	0.201888i	0.987685	−	0.156458i	$-0.0500075\pi$
$613$	33.1608	+	123.758i	0.0540959	+	0.201888i	−0.933589	+	0.358346i	$0.883341\pi$
$614$		0			0
$615$	−286.820	+	165.595i	−0.466374	+	0.269261i
$616$		0			0
$617$	−103.088	−	27.6225i	−0.167080	−	0.0447690i	0.174309	−	0.984691i	$-0.444231\pi$
$617$	−103.088	−	27.6225i	−0.167080	−	0.0447690i	−0.341389	+	0.939922i	$0.610897\pi$
$618$		0			0
$619$	−251.517	−	251.517i	−0.406327	−	0.406327i	0.474128	−	0.880456i	$-0.342763\pi$
$619$	−251.517	−	251.517i	−0.406327	−	0.406327i	−0.880456	+	0.474128i	$0.842763\pi$
$620$		0			0
$621$	244.392	+	141.100i	0.393546	+	0.227214i
$622$		0			0
$623$		−	288.756i		−	0.463493i
$624$		0			0
$625$	780.860			1.24938
$626$		0			0
$627$	30.5359	−	52.8897i	0.0487016	−	0.0843536i
$628$		0			0
$629$	−355.653	+	355.653i	−0.565426	+	0.565426i
$630$		0			0
$631$	103.187	−	385.100i	0.163530	−	0.610301i	−0.834693	−	0.550715i	$-0.814355\pi$
$631$	103.187	−	385.100i	0.163530	−	0.610301i	0.998223	−	0.0595863i	$-0.0189781\pi$
$632$		0			0
$633$	283.172	+	490.468i	0.447349	+	0.774831i
$634$		0			0
$635$	438.461	−	117.485i	0.690490	−	0.185016i
$636$		0			0
$637$	312.808	−	180.600i	0.491065	−	0.283516i
$638$		0			0
$639$	12.7686	+	47.6532i	0.0199822	+	0.0745747i
$640$		0			0
$641$	−248.283	+	143.346i	−0.387337	+	0.223629i	−0.681005	−	0.732278i	$-0.738457\pi$
$641$	−248.283	+	143.346i	−0.387337	+	0.223629i	0.293669	+	0.955907i	$0.405124\pi$
$642$		0			0
$643$	−837.927	−	224.522i	−1.30315	−	0.349179i	−0.460511	−	0.887654i	$-0.652334\pi$
$643$	−837.927	−	224.522i	−1.30315	−	0.349179i	−0.842641	+	0.538475i	$0.819000\pi$
$644$		0			0
$645$	−619.808	−	619.808i	−0.960942	−	0.960942i
$646$		0			0
$647$	856.944	+	494.757i	1.32449	+	0.764694i	0.984441	−	0.175714i	$-0.0562235\pi$
$647$	856.944	+	494.757i	1.32449	+	0.764694i	0.340047	+	0.940408i	$0.389557\pi$
$648$		0			0
$649$		−	271.677i		−	0.418609i
$650$		0			0
$651$	−65.2820			−0.100280
$652$		0			0
$653$	67.5692	−	117.033i	0.103475	−	0.179224i	−0.809639	−	0.586928i	$-0.800337\pi$
$653$	67.5692	−	117.033i	0.103475	−	0.179224i	0.913114	+	0.407704i	$0.133670\pi$
$654$		0			0
$655$	213.851	−	213.851i	0.326490	−	0.326490i
$656$		0			0
$657$	−27.1391	+	101.285i	−0.0413077	+	0.154162i
$658$		0			0
$659$	618.512	+	1071.29i	0.938561	+	1.62563i	0.768158	+	0.640260i	$0.221174\pi$
$659$	618.512	+	1071.29i	0.938561	+	1.62563i	0.170403	+	0.985375i	$0.445493\pi$
$660$		0			0
$661$	−89.8083	+	24.0641i	−0.135867	+	0.0364055i	−0.326112	−	0.945331i	$-0.605739\pi$
$661$	−89.8083	+	24.0641i	−0.135867	+	0.0364055i	0.190244	+	0.981737i	$0.439072\pi$
$662$		0			0
$663$	354.825	+	204.858i	0.535181	+	0.308987i
$664$		0			0
$665$	48.7987	+	182.119i	0.0733815	+	0.273863i
$666$		0			0
$667$	96.7250	−	55.8442i	0.145015	−	0.0837245i
$668$		0			0
$669$	−861.908	−	230.947i	−1.28835	−	0.345213i
$670$		0			0
$671$	446.210	+	446.210i	0.664993	+	0.664993i
$672$		0			0
$673$	242.210	+	139.840i	0.359895	+	0.207786i	0.669035	−	0.743231i	$-0.266708\pi$
$673$	242.210	+	139.840i	0.359895	+	0.207786i	−0.309140	+	0.951017i	$0.600041\pi$
$674$		0			0
$675$		−	377.779i		−	0.559673i
$676$		0			0
$677$	1115.38			1.64754			0.823770	−	0.566924i	$-0.191867\pi$
$677$	1115.38			1.64754			0.823770	+	0.566924i	$0.191867\pi$
$678$		0			0
$679$	−339.335	+	587.745i	−0.499756	+	0.865603i
$680$		0			0
$681$	469.440	−	469.440i	0.689339	−	0.689339i
$682$		0			0
$683$	−220.046	+	821.221i	−0.322175	+	1.20237i	0.594946	+	0.803765i	$0.297173\pi$
$683$	−220.046	+	821.221i	−0.322175	+	1.20237i	−0.917121	+	0.398608i	$0.869493\pi$
$684$		0			0
$685$	219.418	+	380.043i	0.320318	+	0.554807i
$686$		0			0
$687$	−282.636	+	75.7321i	−0.411406	+	0.110236i
$688$		0			0
$689$	−511.975	+	886.767i	−0.743070	+	1.28703i
$690$		0			0
$691$	142.754	+	532.764i	0.206590	+	0.771004i	0.988959	+	0.148189i	$0.0473445\pi$
$691$	142.754	+	532.764i	0.206590	+	0.771004i	−0.782369	+	0.622815i	$0.785989\pi$
$692$		0			0
$693$	74.7668	−	43.1666i	0.107889	−	0.0622895i
$694$		0			0
$695$	−689.267	−	184.688i	−0.991750	−	0.265739i
$696$		0			0
$697$	160.149	+	160.149i	0.229769	+	0.229769i
$698$		0			0
$699$	−720.673	−	416.081i	−1.03101	−	0.595251i
$700$		0			0
$701$			650.323i			0.927707i	0.885912	+	0.463854i	$0.153534\pi$
$701$			650.323i			0.927707i	−0.885912	+	0.463854i	$0.846466\pi$
$702$		0			0
$703$	151.937			0.216127
$704$		0			0
$705$	3.82309	−	6.62178i	0.00542282	−	0.00939259i
$706$		0			0
$707$	−210.637	+	210.637i	−0.297931	+	0.297931i
$708$		0			0
$709$	135.185	−	504.518i	0.190670	−	0.711591i	−0.802675	−	0.596416i	$-0.796591\pi$
$709$	135.185	−	504.518i	0.190670	−	0.711591i	0.993345	−	0.115174i	$-0.0367426\pi$
$710$		0			0
$711$	63.5448	+	110.063i	0.0893739	+	0.154800i
$712$		0			0
$713$	−25.8231	+	6.91927i	−0.0362175	+	0.00970445i
$714$		0			0
$715$	257.450	+	445.917i	0.360070	+	0.623659i
$716$		0			0
$717$	250.655	+	935.458i	0.349589	+	1.30468i
$718$		0			0
$719$	74.3806	−	42.9437i	0.103450	−	0.0597269i	−0.447382	−	0.894343i	$-0.647644\pi$
$719$	74.3806	−	42.9437i	0.103450	−	0.0597269i	0.550832	+	0.834616i	$0.314310\pi$
$720$		0			0
$721$	−1517.02	−	406.483i	−2.10405	−	0.563777i
$722$		0			0
$723$	−86.9474	−	86.9474i	−0.120259	−	0.120259i
$724$		0			0
$725$	−129.485	−	74.7583i	−0.178600	−	0.103115i
$726$		0			0
$727$			460.974i			0.634077i	0.948413	+	0.317039i	$0.102689\pi$
$727$			460.974i			0.634077i	−0.948413	+	0.317039i	$0.897311\pi$
$728$		0			0
$729$	807.323			1.10744
$730$		0			0
$731$	−299.711	+	519.115i	−0.410002	+	0.710144i
$732$		0			0
$733$	631.319	−	631.319i	0.861281	−	0.861281i	−0.130206	−	0.991487i	$-0.541564\pi$
$733$	631.319	−	631.319i	0.861281	−	0.861281i	0.991487	+	0.130206i	$0.0415640\pi$
$734$		0			0
$735$	121.308	−	452.729i	0.165045	−	0.615958i
$736$		0			0
$737$	247.520	+	428.718i	0.335849	+	0.581707i
$738$		0			0
$739$	794.424	−	212.865i	1.07500	−	0.288045i	0.322453	−	0.946585i	$-0.395492\pi$
$739$	794.424	−	212.865i	1.07500	−	0.288045i	0.752546	+	0.658540i	$0.228826\pi$
$740$		0			0
$741$	−32.0333	−	119.550i	−0.0432299	−	0.161336i
$742$		0			0
$743$	−209.252	−	780.941i	−0.281632	−	1.05106i	−0.951266	−	0.308373i	$-0.900216\pi$
$743$	−209.252	−	780.941i	−0.281632	−	1.05106i	0.669634	−	0.742692i	$-0.266451\pi$
$744$		0			0
$745$	−1456.44	+	840.877i	−1.95495	+	1.12869i
$746$		0			0
$747$	145.851	+	39.0807i	0.195249	+	0.0523169i
$748$		0			0
$749$	503.962	+	503.962i	0.672846	+	0.672846i
$750$		0			0
$751$	407.585	+	235.319i	0.542723	+	0.313341i	0.746182	−	0.665742i	$-0.231885\pi$
$751$	407.585	+	235.319i	0.542723	+	0.313341i	−0.203459	+	0.979083i	$0.565218\pi$
$752$		0			0
$753$			367.128i			0.487554i
$754$		0			0
$755$	−576.270			−0.763272
$756$		0			0
$757$	−310.415	+	537.655i	−0.410060	+	0.710245i	−0.994896	−	0.100907i	$-0.967826\pi$
$757$	−310.415	+	537.655i	−0.410060	+	0.710245i	0.584836	+	0.811152i	$0.301159\pi$
$758$		0			0
$759$	−121.492	+	121.492i	−0.160069	+	0.160069i
$760$		0			0
$761$	−50.9559	+	190.170i	−0.0669591	+	0.249895i	−0.991290	−	0.131697i	$-0.957957\pi$
$761$	−50.9559	+	190.170i	−0.0669591	+	0.249895i	0.924331	+	0.381592i	$0.124624\pi$
$762$		0			0
$763$	−0.119201	−	0.206462i	−0.000156227	−	0.000270592i
$764$		0			0
$765$	−105.672	+	28.3147i	−0.138133	+	0.0370126i
$766$		0			0
$767$	−389.317	−	389.317i	−0.507584	−	0.507584i
$768$		0			0
$769$	112.701	+	420.604i	0.146555	+	0.546950i	0.999681	+	0.0252457i	$0.00803682\pi$
$769$	112.701	+	420.604i	0.146555	+	0.546950i	−0.853127	+	0.521704i	$0.825297\pi$
$770$		0			0
$771$	773.790	−	446.748i	1.00362	−	0.579440i
$772$		0			0
$773$	−8.31862	−	2.22897i	−0.0107615	−	0.00288353i	0.253434	−	0.967353i	$-0.418440\pi$
$773$	−8.31862	−	2.22897i	−0.0107615	−	0.00288353i	−0.264196	+	0.964469i	$0.585107\pi$
$774$		0			0
$775$	25.3064	+	25.3064i	0.0326535	+	0.0326535i
$776$		0			0
$777$	−903.955	−	521.899i	−1.16339	−	0.671684i
$778$		0			0
$779$		−	68.4167i		−	0.0878263i
$780$		0			0
$781$	−206.046			−0.263823
$782$		0			0
$783$	163.962	−	283.990i	0.209402	−	0.362694i
$784$		0			0
$785$	−208.461	+	208.461i	−0.265555	+	0.265555i
$786$		0			0
$787$	115.617	−	431.489i	0.146909	−	0.548271i	−0.852754	−	0.522312i	$-0.825070\pi$
$787$	115.617	−	431.489i	0.146909	−	0.548271i	0.999663	−	0.0259585i	$-0.00826376\pi$
$788$		0			0
$789$	−616.540	−	1067.88i	−0.781419	−	1.35346i
$790$		0			0
$791$	−778.860	+	208.695i	−0.984653	+	0.263837i
$792$		0			0
$793$	1278.85			1.61267
$794$		0			0
$795$	343.892	+	1283.42i	0.432568	+	1.61437i
$796$		0			0
$797$	352.061	−	203.263i	0.441733	−	0.255035i	−0.262599	−	0.964905i	$-0.584580\pi$
$797$	352.061	−	203.263i	0.441733	−	0.255035i	0.704333	+	0.709870i	$0.251246\pi$
$798$		0			0
$799$	−5.05067	−	1.35332i	−0.00632124	−	0.00169377i
$800$		0			0
$801$	−35.7884	−	35.7884i	−0.0446796	−	0.0446796i
$802$		0			0
$803$	−379.268	−	218.970i	−0.472314	−	0.272690i
$804$		0			0
$805$		−	530.438i		−	0.658930i
$806$		0			0
$807$	−428.133			−0.530525
$808$		0			0
$809$	−17.4634	+	30.2475i	−0.0215864	+	0.0373888i	−0.876617	−	0.481189i	$-0.840205\pi$
$809$	−17.4634	+	30.2475i	−0.0215864	+	0.0373888i	0.855030	+	0.518578i	$0.173538\pi$
$810$		0			0
$811$	−755.708	+	755.708i	−0.931822	+	0.931822i	−0.997820	−	0.0659978i	$-0.978977\pi$
$811$	−755.708	+	755.708i	−0.931822	+	0.931822i	0.0659978	+	0.997820i	$0.478977\pi$
$812$		0			0
$813$	−180.914	+	675.181i	−0.222527	+	0.830481i
$814$		0			0
$815$	−194.215	−	336.391i	−0.238301	−	0.412750i
$816$		0			0
$817$	174.904	−	46.8653i	0.214081	−	0.0573627i
$818$		0			0
$819$	45.2834	−	169.000i	0.0552911	−	0.206349i
$820$		0			0
$821$	−254.210	−	948.724i	−0.309634	−	1.15557i	−0.928882	−	0.370375i	$-0.879229\pi$
$821$	−254.210	−	948.724i	−0.309634	−	1.15557i	0.619248	−	0.785196i	$-0.287438\pi$
$822$		0			0
$823$	1146.14	−	661.726i	1.39264	−	0.804041i	0.399033	−	0.916937i	$-0.369346\pi$
$823$	1146.14	−	661.726i	1.39264	−	0.804041i	0.993607	+	0.112896i	$0.0360127\pi$
$824$		0			0
$825$	222.172	+	59.5307i	0.269299	+	0.0721585i
$826$		0			0
$827$	−51.7691	−	51.7691i	−0.0625987	−	0.0625987i	0.675114	−	0.737713i	$-0.264094\pi$
$827$	−51.7691	−	51.7691i	−0.0625987	−	0.0625987i	−0.737713	+	0.675114i	$0.764094\pi$
$828$		0			0
$829$	−21.9059	−	12.6474i	−0.0264245	−	0.0152562i	0.486730	−	0.873553i	$-0.338190\pi$
$829$	−21.9059	−	12.6474i	−0.0264245	−	0.0152562i	−0.513154	+	0.858297i	$0.671523\pi$
$830$		0			0
$831$			182.627i			0.219768i
$832$		0			0
$833$	−320.520			−0.384778
$834$		0			0
$835$	−563.822	+	976.568i	−0.675236	+	1.16954i
$836$		0			0
$837$	−55.5026	+	55.5026i	−0.0663113	+	0.0663113i
$838$		0			0
$839$	232.757	−	868.661i	0.277422	−	1.03535i	−0.676779	−	0.736186i	$-0.736625\pi$
$839$	232.757	−	868.661i	0.277422	−	1.03535i	0.954201	−	0.299166i	$-0.0967086\pi$
$840$		0			0
$841$	355.608	+	615.931i	0.422839	+	0.732379i
$842$		0			0
$843$	414.356	−	111.026i	0.491525	−	0.131704i
$844$		0			0
$845$	1007.93	+	270.075i	1.19282	+	0.319615i
$846$		0			0
$847$	−181.099	−	675.869i	−0.213812	−	0.797956i
$848$		0			0
$849$	112.550	−	64.9808i	0.132568	−	0.0765380i
$850$		0			0
$851$	−412.886	−	110.633i	−0.485178	−	0.130003i
$852$		0			0
$853$	−702.043	−	702.043i	−0.823028	−	0.823028i	0.163513	−	0.986541i	$-0.447717\pi$
$853$	−702.043	−	702.043i	−0.823028	−	0.823028i	−0.986541	+	0.163513i	$0.947717\pi$
$854$		0			0
$855$	28.6199	+	16.5237i	0.0334736	+	0.0193260i
$856$		0			0
$857$		−	959.663i		−	1.11979i	−0.828563	−	0.559897i	$-0.810841\pi$
$857$		−	959.663i		−	1.11979i	0.828563	−	0.559897i	$-0.189159\pi$
$858$		0			0
$859$	1526.98			1.77763			0.888813	−	0.458270i	$-0.151531\pi$
$859$	1526.98			1.77763			0.888813	+	0.458270i	$0.151531\pi$
$860$		0			0
$861$	−235.009	+	407.047i	−0.272949	+	0.472761i
$862$		0			0
$863$	149.604	−	149.604i	0.173353	−	0.173353i	−0.615098	−	0.788451i	$-0.710883\pi$
$863$	149.604	−	149.604i	0.173353	−	0.173353i	0.788451	+	0.615098i	$0.210883\pi$
$864$		0			0
$865$	451.850	−	1686.33i	0.522370	−	1.94951i
$866$		0			0
$867$	212.995	+	368.918i	0.245669	+	0.425511i
$868$		0			0
$869$	−512.708	+	137.380i	−0.589997	+	0.158089i
$870$		0			0
$871$	969.058	+	259.658i	1.11258	+	0.298115i
$872$		0			0
$873$	30.7879	+	114.902i	0.0352668	+	0.131617i
$874$		0			0
$875$	556.450	−	321.267i	0.635943	−	0.367162i
$876$		0			0
$877$	1180.45	+	316.301i	1.34601	+	0.360662i	0.858660	−	0.512545i	$-0.171297\pi$
$877$	1180.45	+	316.301i	1.34601	+	0.360662i	0.487349	+	0.873207i	$0.337964\pi$
$878$		0			0
$879$	−16.7372	−	16.7372i	−0.0190412	−	0.0190412i
$880$		0			0
$881$	321.323	+	185.516i	0.364725	+	0.210574i	0.671152	−	0.741320i	$-0.265800\pi$
$881$	321.323	+	185.516i	0.364725	+	0.210574i	−0.306426	+	0.951894i	$0.599133\pi$
$882$		0			0
$883$		−	1407.20i		−	1.59365i	−0.604208	−	0.796827i	$-0.706510\pi$
$883$		−	1407.20i		−	1.59365i	0.604208	−	0.796827i	$-0.293490\pi$
$884$		0			0
$885$	−714.438			−0.807275
$886$		0			0
$887$	−258.623	+	447.948i	−0.291571	+	0.505015i	−0.974181	−	0.225767i	$-0.927511\pi$
$887$	−258.623	+	447.948i	−0.291571	+	0.505015i	0.682611	+	0.730782i	$0.260845\pi$
$888$		0			0
$889$	455.520	−	455.520i	0.512396	−	0.512396i
$890$		0			0
$891$	−107.614	+	401.622i	−0.120779	+	0.450754i
$892$		0			0
$893$	0.789764	+	1.36791i	0.000884395	+	0.00153182i
$894$		0			0
$895$	−1783.01	+	477.755i	−1.99219	+	0.533805i
$896$		0			0
$897$			348.200i			0.388183i
$898$		0			0
$899$	8.04036	+	30.0070i	0.00894367	+	0.0333782i
$900$		0			0
$901$	786.896	−	454.315i	0.873359	−	0.504234i
$902$		0			0
$903$	−1201.58	−	321.962i	−1.33065	−	0.356547i
$904$		0			0
$905$	−1305.79	−	1305.79i	−1.44287	−	1.44287i
$906$		0			0
$907$	−1299.20	−	750.093i	−1.43241	−	0.827005i	−0.435110	−	0.900377i	$-0.643290\pi$
$907$	−1299.20	−	750.093i	−1.43241	−	0.827005i	−0.997305	+	0.0733725i	$0.976624\pi$
$908$		0			0
$909$			52.2126i			0.0574396i
$910$		0			0
$911$	−663.346			−0.728151			−0.364076	−	0.931369i	$-0.618615\pi$
$911$	−663.346			−0.728151			−0.364076	+	0.931369i	$0.618615\pi$
$912$		0			0
$913$	−315.321	+	546.151i	−0.345367	+	0.598194i
$914$		0			0
$915$	1173.41	−	1173.41i	1.28242	−	1.28242i
$916$		0			0
$917$	111.086	−	414.578i	0.121141	−	0.452103i
$918$		0			0
$919$	51.1596	+	88.6110i	0.0556687	+	0.0964211i	0.892517	−	0.451014i	$-0.148938\pi$
$919$	51.1596	+	88.6110i	0.0556687	+	0.0964211i	−0.836848	+	0.547435i	$0.815604\pi$
$920$		0			0
$921$	851.726	−	228.219i	0.924783	−	0.247795i
$922$		0			0
$923$	−295.267	+	295.267i	−0.319899	+	0.319899i
$924$		0			0
$925$	148.103	+	552.729i	0.160112	+	0.597545i
$926$		0			0
$927$	−238.398	+	137.639i	−0.257171	+	0.148478i
$928$		0			0
$929$	−31.5737	−	8.46014i	−0.0339867	−	0.00910672i	0.241786	−	0.970330i	$-0.422267\pi$
$929$	−31.5737	−	8.46014i	−0.0339867	−	0.00910672i	−0.275772	+	0.961223i	$0.588934\pi$
$930$		0			0
$931$	68.4641	+	68.4641i	0.0735382	+	0.0735382i
$932$		0			0
$933$	−183.315	−	105.837i	−0.196479	−	0.113437i
$934$		0			0
$935$		−	456.910i		−	0.488674i
$936$		0			0
$937$	−196.615			−0.209835			−0.104917	−	0.994481i	$-0.533458\pi$
$937$	−196.615			−0.209835			−0.104917	+	0.994481i	$0.533458\pi$
$938$		0			0
$939$	−226.329	+	392.014i	−0.241032	+	0.417480i
$940$		0			0
$941$	269.659	−	269.659i	0.286566	−	0.286566i	−0.549155	−	0.835721i	$-0.685050\pi$
$941$	269.659	−	269.659i	0.286566	−	0.286566i	0.835721	+	0.549155i	$0.185050\pi$
$942$		0			0
$943$	−49.8174	+	185.921i	−0.0528287	+	0.197159i
$944$		0			0
$945$	−778.697	−	1348.74i	−0.824018	−	1.42724i
$946$		0			0
$947$	1237.89	−	331.692i	1.30717	−	0.350255i	0.463013	−	0.886351i	$-0.346768\pi$
$947$	1237.89	−	331.692i	1.30717	−	0.350255i	0.844157	+	0.536096i	$0.180102\pi$
$948$		0			0
$949$	−857.283	+	229.708i	−0.903354	+	0.242053i
$950$		0			0
$951$	−97.0544	−	362.212i	−0.102055	−	0.380875i
$952$		0			0
$953$	1142.09	−	659.387i	1.19842	−	0.691907i	0.238215	−	0.971212i	$-0.423438\pi$
$953$	1142.09	−	659.387i	1.19842	−	0.691907i	0.960202	+	0.279306i	$0.0901042\pi$
$954$		0			0
$955$	1407.55	+	377.152i	1.47387	+	0.394924i
$956$		0			0
$957$	141.177	+	141.177i	0.147520	+	0.147520i
$958$		0			0
$959$	539.347	+	311.392i	0.562406	+	0.324705i
$960$		0			0
$961$			953.564i			0.992262i
$962$		0			0
$963$	124.922			0.129721
$964$		0			0
$965$	−998.636	+	1729.69i	−1.03486	+	1.79242i
$966$		0			0
$967$	879.683	−	879.683i	0.909703	−	0.909703i	−0.0865445	−	0.996248i	$-0.527582\pi$
$967$	879.683	−	879.683i	0.909703	−	0.909703i	0.996248	+	0.0865445i	$0.0275825\pi$
$968$		0			0
$969$	−28.4256	+	106.086i	−0.0293350	+	0.109480i
$970$		0			0
$971$	−23.1366	−	40.0737i	−0.0238276	−	0.0412705i	0.853866	−	0.520493i	$-0.174252\pi$
$971$	−23.1366	−	40.0737i	−0.0238276	−	0.0412705i	−0.877693	+	0.479223i	$0.840919\pi$
$972$		0			0
$973$	−978.190	+	262.105i	−1.00533	+	0.269378i
$974$		0			0
$975$	403.683	−	233.067i	0.414034	−	0.239043i
$976$		0			0
$977$	−411.992	−	1537.57i	−0.421691	−	1.57377i	−0.771045	−	0.636780i	$-0.780266\pi$
$977$	−411.992	−	1537.57i	−0.421691	−	1.57377i	0.349355	−	0.936991i	$-0.386401\pi$
$978$		0			0
$979$	183.064	−	105.692i	0.186991	−	0.107959i
$980$		0			0
$981$	−0.0403626	−	0.0108151i	−4.11443e−5	−	1.10246e-5i
$982$		0			0
$983$	−632.213	−	632.213i	−0.643146	−	0.643146i	0.308181	−	0.951328i	$-0.400280\pi$
$983$	−632.213	−	632.213i	−0.643146	−	0.643146i	−0.951328	+	0.308181i	$0.900280\pi$
$984$		0			0
$985$	1283.25	+	740.886i	1.30279	+	0.752169i
$986$		0			0
$987$		−	10.8513i		−	0.0109942i
$988$		0			0
$989$	−509.423			−0.515089
$990$		0			0
$991$	600.733	−	1040.50i	0.606188	−	1.04995i	−0.385674	−	0.922635i	$-0.626031\pi$
$991$	600.733	−	1040.50i	0.606188	−	1.04995i	0.991862	−	0.127314i	$-0.0406355\pi$
$992$		0			0
$993$	585.205	−	585.205i	0.589330	−	0.589330i
$994$		0			0
$995$	82.2046	−	306.792i	0.0826177	−	0.308333i
$996$		0			0
$997$	242.817	+	420.572i	0.243548	+	0.421837i	0.961722	−	0.274026i	$-0.0883554\pi$
$997$	242.817	+	420.572i	0.243548	+	0.421837i	−0.718174	+	0.695863i	$0.755022\pi$
$998$		0			0
$999$	−1212.26	+	324.823i	−1.21347	+	0.325148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.d.97.1		4
4.3	odd	2		13.3.f.a.6.1	✓	4
12.11	even	2		117.3.bd.b.19.1		4
13.11	odd	12	inner	208.3.bd.d.193.1		4
20.3	even	4		325.3.w.a.149.1		4
20.7	even	4		325.3.w.b.149.1		4
20.19	odd	2		325.3.t.a.201.1		4
52.3	odd	6		169.3.f.c.80.1		4
52.7	even	12		169.3.d.a.99.1		4
52.11	even	12		13.3.f.a.11.1	yes	4
52.15	even	12		169.3.f.b.89.1		4
52.19	even	12		169.3.d.c.99.2		4
52.23	odd	6		169.3.f.a.80.1		4
52.31	even	4		169.3.f.a.150.1		4
52.35	odd	6		169.3.d.a.70.1		4
52.43	odd	6		169.3.d.c.70.2		4
52.47	even	4		169.3.f.c.150.1		4
52.51	odd	2		169.3.f.b.19.1		4
156.11	odd	12		117.3.bd.b.37.1		4
260.63	odd	12		325.3.w.b.24.1		4
260.167	odd	12		325.3.w.a.24.1		4
260.219	even	12		325.3.t.a.76.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.6.1	✓	4	4.3	odd	2
13.3.f.a.11.1	yes	4	52.11	even	12
117.3.bd.b.19.1		4	12.11	even	2
117.3.bd.b.37.1		4	156.11	odd	12
169.3.d.a.70.1		4	52.35	odd	6
169.3.d.a.99.1		4	52.7	even	12
169.3.d.c.70.2		4	52.43	odd	6
169.3.d.c.99.2		4	52.19	even	12
169.3.f.a.80.1		4	52.23	odd	6
169.3.f.a.150.1		4	52.31	even	4
169.3.f.b.19.1		4	52.51	odd	2
169.3.f.b.89.1		4	52.15	even	12
169.3.f.c.80.1		4	52.3	odd	6
169.3.f.c.150.1		4	52.47	even	4
208.3.bd.d.97.1		4	1.1	even	1	trivial
208.3.bd.d.193.1		4	13.11	odd	12	inner
325.3.t.a.76.1		4	260.219	even	12
325.3.t.a.201.1		4	20.19	odd	2
325.3.w.a.24.1		4	260.167	odd	12
325.3.w.a.149.1		4	20.3	even	4
325.3.w.b.24.1		4	260.63	odd	12
325.3.w.b.149.1		4	20.7	even	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 2.36603i) q^{3} +(-4.36603 + 4.36603i) q^{5} +(-2.26795 + 8.46410i) q^{7} +(0.767949 + 1.33013i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 2.36603i) q^{3} +(-4.36603 + 4.36603i) q^{5} +(-2.26795 + 8.46410i) q^{7} +(0.767949 + 1.33013i) q^{9} +(-6.19615 + 1.66025i) q^{11} +(-6.50000 + 11.2583i) q^{13} +(4.36603 + 16.2942i) q^{15} +(9.99038 - 5.76795i) q^{17} +(-3.36603 - 0.901924i) q^{19} +(16.9282 + 16.9282i) q^{21} +(8.49038 + 4.90192i) q^{23} -13.1244i q^{25} +28.7846 q^{27} +(5.69615 - 9.86603i) q^{29} +(-1.92820 + 1.92820i) q^{31} +(-4.53590 + 16.9282i) q^{33} +(-27.0526 - 46.8564i) q^{35} +(-42.1147 + 11.2846i) q^{37} +(17.7583 + 30.7583i) q^{39} +(5.08142 + 18.9641i) q^{41} +(-45.0000 + 25.9808i) q^{43} +(-9.16025 - 2.45448i) q^{45} +(-0.320508 - 0.320508i) q^{47} +(-24.0622 - 13.8923i) q^{49} -31.5167i q^{51} +78.7654 q^{53} +(19.8038 - 34.3013i) q^{55} +(-6.73205 + 6.73205i) q^{57} +(-10.9615 + 40.9090i) q^{59} +(-49.1865 - 85.1936i) q^{61} +(-13.0000 + 3.48334i) q^{63} +(-20.7750 - 77.5333i) q^{65} +(-19.9737 - 74.5429i) q^{67} +(23.1962 - 13.3923i) q^{69} +(31.0263 + 8.31347i) q^{71} +(48.2750 + 48.2750i) q^{73} +(-31.0526 - 17.9282i) q^{75} -56.2102i q^{77} +82.7461 q^{79} +(32.4090 - 56.1340i) q^{81} +(69.5167 - 69.5167i) q^{83} +(-18.4352 + 68.8013i) q^{85} +(-15.5622 - 26.9545i) q^{87} +(-31.8301 + 8.52886i) q^{89} +(-80.5500 - 80.5500i) q^{91} +(1.92820 + 7.19615i) q^{93} +(18.6340 - 10.7583i) q^{95} +(74.8109 + 20.0455i) q^{97} +(-6.96668 - 6.96668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9	\( 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9} - 4 q^{11} - 26 q^{13} + 14 q^{15} - 12 q^{17} - 10 q^{19} + 40 q^{21} - 18 q^{23} + 32 q^{27} + 2 q^{29} + 20 q^{31} - 32 q^{33} - 32 q^{35} - 68 q^{37} + 26 q^{39} + 100 q^{41} - 180 q^{43} - 2 q^{45} + 68 q^{47} - 72 q^{49} + 128 q^{53} + 100 q^{55} - 20 q^{57} + 164 q^{59} - 124 q^{61} - 52 q^{63} + 52 q^{65} - 118 q^{67} + 72 q^{69} + 86 q^{71} + 58 q^{73} - 48 q^{75} + 40 q^{79} - 2 q^{81} + 188 q^{83} + 96 q^{85} - 38 q^{87} - 110 q^{89} - 52 q^{91} - 20 q^{93} + 78 q^{95} + 178 q^{97} - 208 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9 - 4 * q^11 - 26 * q^13 + 14 * q^15 - 12 * q^17 - 10 * q^19 + 40 * q^21 - 18 * q^23 + 32 * q^27 + 2 * q^29 + 20 * q^31 - 32 * q^33 - 32 * q^35 - 68 * q^37 + 26 * q^39 + 100 * q^41 - 180 * q^43 - 2 * q^45 + 68 * q^47 - 72 * q^49 + 128 * q^53 + 100 * q^55 - 20 * q^57 + 164 * q^59 - 124 * q^61 - 52 * q^63 + 52 * q^65 - 118 * q^67 + 72 * q^69 + 86 * q^71 + 58 * q^73 - 48 * q^75 + 40 * q^79 - 2 * q^81 + 188 * q^83 + 96 * q^85 - 38 * q^87 - 110 * q^89 - 52 * q^91 - 20 * q^93 + 78 * q^95 + 178 * q^97 - 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more