LMFDB - Embedded newform 168.3.z.b.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,3,Mod(73,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("168.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	168.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.35911766016.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 78x^{4} - 18x^{3} - 153x^{2} - 230x + 529 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 78x^4 - 18x^3 - 153x^2 - 230*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.4
Root			$-1.33172 + 1.34622i$ of defining polynomial
Character	$\chi$	$=$	168.73
Dual form			168.3.z.b.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{3} +(5.30550 - 3.06313i) q^{5} +(0.664986 + 6.96834i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.89129 - 3.27581i) q^{11} -9.29319i q^{13} +10.6110 q^{15} +(5.84742 + 3.37601i) q^{17} +(5.71544 - 3.29981i) q^{19} +(-5.03728 + 11.0284i) q^{21} +(19.5920 + 33.9344i) q^{23} +(6.26557 - 10.8523i) q^{25} +5.19615i q^{27} -6.57302 q^{29} +(-18.9941 - 10.9662i) q^{31} +(5.67386 - 3.27581i) q^{33} +(24.8730 + 34.9336i) q^{35} +(-33.5334 - 58.0816i) q^{37} +(8.04814 - 13.9398i) q^{39} -53.6570i q^{41} -42.0426 q^{43} +(15.9165 + 9.18940i) q^{45} +(-49.8304 + 28.7696i) q^{47} +(-48.1156 + 9.26770i) q^{49} +(5.84742 + 10.1280i) q^{51} +(5.71091 - 9.89159i) q^{53} -23.1731i q^{55} +11.4309 q^{57} +(54.0433 + 31.2019i) q^{59} +(-103.607 + 59.8176i) q^{61} +(-17.1068 + 12.1802i) q^{63} +(-28.4663 - 49.3051i) q^{65} +(27.8740 - 48.2792i) q^{67} +67.8687i q^{69} -131.158 q^{71} +(66.7208 + 38.5213i) q^{73} +(18.7967 - 10.8523i) q^{75} +(24.0846 + 11.0008i) q^{77} +(-74.7467 - 129.465i) q^{79} +(-4.50000 + 7.79423i) q^{81} -39.7649i q^{83} +41.3647 q^{85} +(-9.85953 - 5.69240i) q^{87} +(48.4984 - 28.0006i) q^{89} +(64.7582 - 6.17984i) q^{91} +(-18.9941 - 32.8987i) q^{93} +(20.2155 - 35.0143i) q^{95} +142.413i q^{97} +11.3477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 6 q^{5} + 8 q^{7} + 12 q^{9} - 22 q^{11} - 12 q^{15} + 36 q^{17} + 42 q^{19} + 6 q^{21} + 48 q^{23} + 42 q^{25} + 68 q^{29} - 60 q^{31} - 66 q^{33} - 12 q^{35} - 118 q^{37} - 18 q^{39}+ \cdots - 132 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 6 * q^5 + 8 * q^7 + 12 * q^9 - 22 * q^11 - 12 * q^15 + 36 * q^17 + 42 * q^19 + 6 * q^21 + 48 * q^23 + 42 * q^25 + 68 * q^29 - 60 * q^31 - 66 * q^33 - 12 * q^35 - 118 * q^37 - 18 * q^39 - 92 * q^43 - 18 * q^45 - 12 * q^47 - 20 * q^49 + 36 * q^51 + 10 * q^53 + 84 * q^57 - 54 * q^59 + 24 * q^61 - 6 * q^63 - 148 * q^65 + 22 * q^67 - 392 * q^71 - 138 * q^73 + 126 * q^75 - 126 * q^77 + 164 * q^79 - 36 * q^81 + 200 * q^85 + 102 * q^87 - 60 * q^89 + 90 * q^91 - 60 * q^93 - 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	5.30550	−	3.06313i	1.06110	−	0.612627i	0.135364	−	0.990796i	$-0.456780\pi$
$5$	5.30550	−	3.06313i	1.06110	−	0.612627i	0.925736	+	0.378169i	$0.123446\pi$
$6$		0			0
$7$	0.664986	+	6.96834i	0.0949980	+	0.995477i
$7$	0.664986	+	6.96834i	0.0949980	+	0.995477i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	1.89129	−	3.27581i	0.171935	−	0.297801i	−0.767161	−	0.641454i	$-0.778331\pi$
$11$	1.89129	−	3.27581i	0.171935	−	0.297801i	0.939096	+	0.343654i	$0.111665\pi$
$12$		0			0
$13$		−	9.29319i		−	0.714861i	−0.933940	−	0.357431i	$-0.883653\pi$
$13$		−	9.29319i		−	0.714861i	0.933940	−	0.357431i	$-0.116347\pi$
$14$		0			0
$15$	10.6110			0.707400
$16$		0			0
$17$	5.84742	+	3.37601i	0.343966	+	0.198589i	0.662024	−	0.749482i	$-0.269698\pi$
$17$	5.84742	+	3.37601i	0.343966	+	0.198589i	−0.318059	+	0.948071i	$0.603031\pi$
$18$		0			0
$19$	5.71544	−	3.29981i	0.300813	−	0.173674i	−0.341995	−	0.939702i	$-0.611103\pi$
$19$	5.71544	−	3.29981i	0.300813	−	0.173674i	0.642808	+	0.766027i	$0.277769\pi$
$20$		0			0
$21$	−5.03728	+	11.0284i	−0.239871	+	0.525162i
$22$		0			0
$23$	19.5920	+	33.9344i	0.851827	+	1.47541i	0.879558	+	0.475792i	$0.157838\pi$
$23$	19.5920	+	33.9344i	0.851827	+	1.47541i	−0.0277315	+	0.999615i	$0.508828\pi$
$24$		0			0
$25$	6.26557	−	10.8523i	0.250623	−	0.434091i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−6.57302			−0.226656			−0.113328	−	0.993558i	$-0.536151\pi$
$29$	−6.57302			−0.226656			−0.113328	+	0.993558i	$0.536151\pi$
$30$		0			0
$31$	−18.9941	−	10.9662i	−0.612712	−	0.353750i	0.161314	−	0.986903i	$-0.448427\pi$
$31$	−18.9941	−	10.9662i	−0.612712	−	0.353750i	−0.774026	+	0.633153i	$0.781760\pi$
$32$		0			0
$33$	5.67386	−	3.27581i	0.171935	−	0.0992669i
$34$		0			0
$35$	24.8730	+	34.9336i	0.710658	+	0.998103i
$36$		0			0
$37$	−33.5334	−	58.0816i	−0.906309	−	1.56977i	−0.819151	−	0.573578i	$-0.805555\pi$
$37$	−33.5334	−	58.0816i	−0.906309	−	1.56977i	−0.0871580	−	0.996194i	$-0.527779\pi$
$38$		0			0
$39$	8.04814	−	13.9398i	0.206363	−	0.357431i
$40$		0			0
$41$		−	53.6570i		−	1.30871i	−0.756189	−	0.654353i	$-0.772941\pi$
$41$		−	53.6570i		−	1.30871i	0.756189	−	0.654353i	$-0.227059\pi$
$42$		0			0
$43$	−42.0426			−0.977734			−0.488867	−	0.872358i	$-0.662590\pi$
$43$	−42.0426			−0.977734			−0.488867	+	0.872358i	$0.662590\pi$
$44$		0			0
$45$	15.9165	+	9.18940i	0.353700	+	0.204209i
$46$		0			0
$47$	−49.8304	+	28.7696i	−1.06022	+	0.612119i	−0.925494	−	0.378763i	$-0.876350\pi$
$47$	−49.8304	+	28.7696i	−1.06022	+	0.612119i	−0.134728	+	0.990883i	$0.543016\pi$
$48$		0			0
$49$	−48.1156	+	9.26770i	−0.981951	+	0.189137i
$50$		0			0
$51$	5.84742	+	10.1280i	0.114655	+	0.198589i
$52$		0			0
$53$	5.71091	−	9.89159i	0.107753	−	0.186634i	−0.807107	−	0.590406i	$-0.798968\pi$
$53$	5.71091	−	9.89159i	0.107753	−	0.186634i	0.914860	+	0.403772i	$0.132301\pi$
$54$		0			0
$55$		−	23.1731i		−	0.421329i
$56$		0			0
$57$	11.4309			0.200542
$58$		0			0
$59$	54.0433	+	31.2019i	0.915988	+	0.528846i	0.882353	−	0.470588i	$-0.155958\pi$
$59$	54.0433	+	31.2019i	0.915988	+	0.528846i	0.0336351	+	0.999434i	$0.489292\pi$
$60$		0			0
$61$	−103.607	+	59.8176i	−1.69848	+	0.980617i	−0.751271	+	0.659994i	$0.770559\pi$
$61$	−103.607	+	59.8176i	−1.69848	+	0.980617i	−0.947207	+	0.320622i	$0.896108\pi$
$62$		0			0
$63$	−17.1068	+	12.1802i	−0.271537	+	0.193336i
$64$		0			0
$65$	−28.4663	−	49.3051i	−0.437943	−	0.758539i
$66$		0			0
$67$	27.8740	−	48.2792i	0.416030	−	0.720585i	−0.579506	−	0.814968i	$-0.696755\pi$
$67$	27.8740	−	48.2792i	0.416030	−	0.720585i	0.995536	+	0.0943832i	$0.0300879\pi$
$68$		0			0
$69$			67.8687i			0.983605i
$70$		0			0
$71$	−131.158			−1.84730			−0.923648	−	0.383243i	$-0.874807\pi$
$71$	−131.158			−1.84730			−0.923648	+	0.383243i	$0.874807\pi$
$72$		0			0
$73$	66.7208	+	38.5213i	0.913984	+	0.527689i	0.881711	−	0.471790i	$-0.156392\pi$
$73$	66.7208	+	38.5213i	0.913984	+	0.527689i	0.0322732	+	0.999479i	$0.489725\pi$
$74$		0			0
$75$	18.7967	−	10.8523i	0.250623	−	0.144697i
$76$		0			0
$77$	24.0846	+	11.0008i	0.312787	+	0.142867i
$78$		0			0
$79$	−74.7467	−	129.465i	−0.946160	−	1.63880i	−0.753412	−	0.657549i	$-0.771593\pi$
$79$	−74.7467	−	129.465i	−0.946160	−	1.63880i	−0.192749	−	0.981248i	$-0.561740\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	39.7649i		−	0.479096i	−0.970885	−	0.239548i	$-0.923001\pi$
$83$		−	39.7649i		−	0.479096i	0.970885	−	0.239548i	$-0.0769992\pi$
$84$		0			0
$85$	41.3647			0.486643
$86$		0			0
$87$	−9.85953	−	5.69240i	−0.113328	−	0.0654299i
$88$		0			0
$89$	48.4984	−	28.0006i	0.544926	−	0.314613i	−0.202147	−	0.979355i	$-0.564792\pi$
$89$	48.4984	−	28.0006i	0.544926	−	0.314613i	0.747073	+	0.664742i	$0.231459\pi$
$90$		0			0
$91$	64.7582	−	6.17984i	0.711628	−	0.0679104i
$92$		0			0
$93$	−18.9941	−	32.8987i	−0.204237	−	0.353750i
$94$		0			0
$95$	20.2155	−	35.0143i	0.212795	−	0.368572i
$96$		0			0
$97$			142.413i			1.46818i	0.679054	+	0.734089i	$0.262390\pi$
$97$			142.413i			1.46818i	−0.679054	+	0.734089i	$0.737610\pi$
$98$		0			0
$99$	11.3477			0.114624
$100$		0			0
$101$	127.020	+	73.3353i	1.25763	+	0.726092i	0.972613	−	0.232431i	$-0.0746680\pi$
$101$	127.020	+	73.3353i	1.25763	+	0.726092i	0.285015	+	0.958523i	$0.408001\pi$
$102$		0			0
$103$	−6.66772	+	3.84961i	−0.0647351	+	0.0373748i	−0.532018	−	0.846733i	$-0.678566\pi$
$103$	−6.66772	+	3.84961i	−0.0647351	+	0.0373748i	0.467283	+	0.884108i	$0.345233\pi$
$104$		0			0
$105$	7.05617	+	73.9411i	0.0672016	+	0.704201i
$106$		0			0
$107$	69.7970	+	120.892i	0.652308	+	1.12983i	0.982561	+	0.185939i	$0.0595327\pi$
$107$	69.7970	+	120.892i	0.652308	+	1.12983i	−0.330253	+	0.943893i	$0.607134\pi$
$108$		0			0
$109$	75.8059	−	131.300i	0.695467	−	1.20458i	−0.274556	−	0.961571i	$-0.588531\pi$
$109$	75.8059	−	131.300i	0.695467	−	1.20458i	0.970023	−	0.243013i	$-0.0781356\pi$
$110$		0			0
$111$		−	116.163i		−	1.04652i
$112$		0			0
$113$	−40.4809			−0.358238			−0.179119	−	0.983827i	$-0.557325\pi$
$113$	−40.4809			−0.358238			−0.179119	+	0.983827i	$0.557325\pi$
$114$		0			0
$115$	207.891	+	120.026i	1.80775	+	1.04370i
$116$		0			0
$117$	24.1444	−	13.9398i	0.206363	−	0.119144i
$118$		0			0
$119$	−19.6367	+	42.9918i	−0.165015	+	0.361276i
$120$		0			0
$121$	53.3461	+	92.3981i	0.440877	+	0.763621i
$122$		0			0
$123$	46.4683	−	80.4854i	0.377791	−	0.654353i
$124$		0			0
$125$			76.3876i			0.611101i
$126$		0			0
$127$	−88.3367			−0.695565			−0.347782	−	0.937575i	$-0.613065\pi$
$127$	−88.3367			−0.695565			−0.347782	+	0.937575i	$0.613065\pi$
$128$		0			0
$129$	−63.0639	−	36.4099i	−0.488867	−	0.282248i
$130$		0			0
$131$	58.5849	−	33.8240i	0.447213	−	0.258198i	−0.259440	−	0.965759i	$-0.583538\pi$
$131$	58.5849	−	33.8240i	0.447213	−	0.258198i	0.706652	+	0.707561i	$0.250205\pi$
$132$		0			0
$133$	26.7949	+	37.6328i	0.201465	+	0.282954i
$134$		0			0
$135$	15.9165	+	27.5682i	0.117900	+	0.204209i
$136$		0			0
$137$	82.6190	−	143.100i	0.603058	−	1.04453i	−0.389297	−	0.921112i	$-0.627282\pi$
$137$	82.6190	−	143.100i	0.603058	−	1.04453i	0.992355	−	0.123415i	$-0.0393847\pi$
$138$		0			0
$139$		−	73.0610i		−	0.525619i	−0.964848	−	0.262809i	$-0.915351\pi$
$139$		−	73.0610i		−	0.525619i	0.964848	−	0.262809i	$-0.0846490\pi$
$140$		0			0
$141$	−99.6609			−0.706815
$142$		0			0
$143$	−30.4427	−	17.5761i	−0.212886	−	0.122910i
$144$		0			0
$145$	−34.8732	+	20.1340i	−0.240505	+	0.138855i
$146$		0			0
$147$	−80.1994	−	27.7678i	−0.545574	−	0.188896i
$148$		0			0
$149$	−75.2940	−	130.413i	−0.505329	−	0.875255i	−0.999981	−	0.00616430i	$-0.998038\pi$
$149$	−75.2940	−	130.413i	−0.505329	−	0.875255i	0.494652	−	0.869091i	$-0.335296\pi$
$150$		0			0
$151$	−69.4921	+	120.364i	−0.460213	+	0.797112i	−0.998971	−	0.0453486i	$-0.985560\pi$
$151$	−69.4921	+	120.364i	−0.460213	+	0.797112i	0.538759	+	0.842460i	$0.318893\pi$
$152$		0			0
$153$			20.2561i			0.132393i
$154$		0			0
$155$	−134.364			−0.866866
$156$		0			0
$157$	136.184	+	78.6256i	0.867412	+	0.500800i	0.866487	−	0.499199i	$-0.166372\pi$
$157$	136.184	+	78.6256i	0.867412	+	0.500800i	0.000924354		1.00000i	$0.499706\pi$
$158$		0			0
$159$	17.1327	−	9.89159i	0.107753	−	0.0622113i
$160$		0			0
$161$	−223.438	+	159.090i	−1.38781	+	0.988135i
$162$		0			0
$163$	10.6613	+	18.4660i	0.0654069	+	0.113288i	0.896874	−	0.442285i	$-0.145832\pi$
$163$	10.6613	+	18.4660i	0.0654069	+	0.113288i	−0.831467	+	0.555573i	$0.812499\pi$
$164$		0			0
$165$	20.0685	−	34.7596i	0.121627	−	0.210664i
$166$		0			0
$167$		−	177.968i		−	1.06567i	−0.846218	−	0.532837i	$-0.821126\pi$
$167$		−	177.968i		−	1.06567i	0.846218	−	0.532837i	$-0.178874\pi$
$168$		0			0
$169$	82.6365			0.488974
$170$		0			0
$171$	17.1463	+	9.89944i	0.100271	+	0.0578914i
$172$		0			0
$173$	95.3511	−	55.0510i	0.551163	−	0.318214i	−0.198428	−	0.980115i	$-0.563584\pi$
$173$	95.3511	−	55.0510i	0.551163	−	0.318214i	0.749591	+	0.661902i	$0.230250\pi$
$174$		0			0
$175$	79.7889	+	36.4440i	0.455937	+	0.208251i
$176$		0			0
$177$	54.0433	+	93.6057i	0.305329	+	0.528846i
$178$		0			0
$179$	14.1225	−	24.4608i	0.0788964	−	0.136653i	−0.823878	−	0.566768i	$-0.808194\pi$
$179$	14.1225	−	24.4608i	0.0788964	−	0.136653i	0.902774	+	0.430115i	$0.141527\pi$
$180$		0			0
$181$			206.410i			1.14039i	0.821510	+	0.570195i	$0.193132\pi$
$181$			206.410i			1.14039i	−0.821510	+	0.570195i	$0.806868\pi$
$182$		0			0
$183$	−207.214			−1.13232
$184$		0			0
$185$	−355.823	−	205.435i	−1.92337	−	1.11046i
$186$		0			0
$187$	22.1183	−	12.7700i	0.118280	−	0.0682888i
$188$		0			0
$189$	−36.2086	+	3.45537i	−0.191580	+	0.0182824i
$190$		0			0
$191$	31.8684	+	55.1977i	0.166850	+	0.288993i	0.937311	−	0.348494i	$-0.113307\pi$
$191$	31.8684	+	55.1977i	0.166850	+	0.288993i	−0.770460	+	0.637488i	$0.779974\pi$
$192$		0			0
$193$	33.6762	−	58.3288i	0.174488	−	0.302222i	−0.765496	−	0.643441i	$-0.777506\pi$
$193$	33.6762	−	58.3288i	0.174488	−	0.302222i	0.939984	+	0.341219i	$0.110840\pi$
$194$		0			0
$195$		−	98.6101i		−	0.505693i
$196$		0			0
$197$	96.0707			0.487668			0.243834	−	0.969817i	$-0.421595\pi$
$197$	96.0707			0.487668			0.243834	+	0.969817i	$0.421595\pi$
$198$		0			0
$199$	178.392	+	102.995i	0.896444	+	0.517562i	0.876045	−	0.482230i	$-0.160173\pi$
$199$	178.392	+	102.995i	0.896444	+	0.517562i	0.0203995	+	0.999792i	$0.493506\pi$
$200$		0			0
$201$	83.6220	−	48.2792i	0.416030	−	0.240195i
$202$		0			0
$203$	−4.37097	−	45.8030i	−0.0215319	−	0.225631i
$204$		0			0
$205$	−164.358	−	284.677i	−0.801748	−	1.38867i
$206$		0			0
$207$	−58.7760	+	101.803i	−0.283942	+	0.491802i
$208$		0			0
$209$		−	24.9636i		−	0.119443i
$210$		0			0
$211$	−121.942			−0.577925			−0.288963	−	0.957340i	$-0.593310\pi$
$211$	−121.942			−0.577925			−0.288963	+	0.957340i	$0.593310\pi$
$212$		0			0
$213$	−196.737	−	113.586i	−0.923648	−	0.533268i
$214$		0			0
$215$	−223.057	+	128.782i	−1.03747	+	0.598986i
$216$		0			0
$217$	63.7857	−	139.650i	0.293943	−	0.643547i
$218$		0			0
$219$	66.7208	+	115.564i	0.304661	+	0.527689i
$220$		0			0
$221$	31.3739	−	54.3412i	0.141963	−	0.245888i
$222$		0			0
$223$		−	18.5026i		−	0.0829712i	−0.999139	−	0.0414856i	$-0.986791\pi$
$223$		−	18.5026i		−	0.0829712i	0.999139	−	0.0414856i	$-0.0132091\pi$
$224$		0			0
$225$	37.5934			0.167082
$226$		0			0
$227$	−127.348	−	73.5243i	−0.561004	−	0.323896i	0.192545	−	0.981288i	$-0.438326\pi$
$227$	−127.348	−	73.5243i	−0.561004	−	0.323896i	−0.753548	+	0.657393i	$0.771659\pi$
$228$		0			0
$229$	−311.695	+	179.957i	−1.36112	+	0.785840i	−0.989772	−	0.142656i	$-0.954436\pi$
$229$	−311.695	+	179.957i	−1.36112	+	0.785840i	−0.371343	+	0.928496i	$0.621103\pi$
$230$		0			0
$231$	26.6000	+	37.3591i	0.115151	+	0.161728i
$232$		0			0
$233$	−22.0340	−	38.1641i	−0.0945667	−	0.163794i	0.814861	−	0.579656i	$-0.196813\pi$
$233$	−22.0340	−	38.1641i	−0.0945667	−	0.163794i	−0.909428	+	0.415862i	$0.863480\pi$
$234$		0			0
$235$	−176.250	+	305.274i	−0.750001	+	1.29904i
$236$		0			0
$237$		−	258.930i		−	1.09253i
$238$		0			0
$239$	165.077			0.690698			0.345349	−	0.938474i	$-0.387761\pi$
$239$	165.077			0.690698			0.345349	+	0.938474i	$0.387761\pi$
$240$		0			0
$241$	−115.828	−	66.8732i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$241$	−115.828	−	66.8732i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−226.889	+	196.554i	−0.926078	+	0.802262i
$246$		0			0
$247$	−30.6658	−	53.1147i	−0.124153	−	0.215039i
$248$		0			0
$249$	34.4374	−	59.6474i	0.138303	−	0.239548i
$250$		0			0
$251$			403.639i			1.60812i	0.594545	+	0.804062i	$0.297332\pi$
$251$			403.639i			1.60812i	−0.594545	+	0.804062i	$0.702668\pi$
$252$		0			0
$253$	148.217			0.585836
$254$		0			0
$255$	62.0470	+	35.8228i	0.243322	+	0.140482i
$256$		0			0
$257$	242.418	−	139.960i	0.943260	−	0.544592i	0.0522795	−	0.998632i	$-0.483351\pi$
$257$	242.418	−	139.960i	0.943260	−	0.544592i	0.890981	+	0.454041i	$0.150018\pi$
$258$		0			0
$259$	382.433	−	272.296i	1.47658	−	1.05134i
$260$		0			0
$261$	−9.85953	−	17.0772i	−0.0377760	−	0.0654299i
$262$		0			0
$263$	70.9462	−	122.882i	0.269758	−	0.467234i	−0.699042	−	0.715081i	$-0.746390\pi$
$263$	70.9462	−	122.882i	0.269758	−	0.467234i	0.968799	+	0.247847i	$0.0797231\pi$
$264$		0			0
$265$		−	69.9731i		−	0.264050i
$266$		0			0
$267$	96.9968			0.363284
$268$		0			0
$269$	344.508	+	198.902i	1.28070	+	0.739411i	0.976976	−	0.213350i	$-0.0684374\pi$
$269$	344.508	+	198.902i	1.28070	+	0.739411i	0.303722	+	0.952761i	$0.401771\pi$
$270$		0			0
$271$	−378.562	+	218.563i	−1.39691	+	0.806505i	−0.994067	−	0.108765i	$-0.965310\pi$
$271$	−378.562	+	218.563i	−1.39691	+	0.806505i	−0.402840	+	0.915270i	$0.631977\pi$
$272$		0			0
$273$	102.489	+	46.8124i	0.375418	+	0.171474i
$274$		0			0
$275$	−23.7000	−	41.0496i	−0.0861818	−	0.149271i
$276$		0			0
$277$	−2.65404	+	4.59692i	−0.00958136	+	0.0165954i	−0.870776	−	0.491679i	$-0.836383\pi$
$277$	−2.65404	+	4.59692i	−0.00958136	+	0.0165954i	0.861195	+	0.508275i	$0.169717\pi$
$278$		0			0
$279$		−	65.7974i		−	0.235833i
$280$		0			0
$281$	297.662			1.05930			0.529648	−	0.848217i	$-0.322324\pi$
$281$	297.662			1.05930			0.529648	+	0.848217i	$0.322324\pi$
$282$		0			0
$283$	178.296	+	102.939i	0.630020	+	0.363742i	0.780760	−	0.624831i	$-0.214832\pi$
$283$	178.296	+	102.939i	0.630020	+	0.363742i	−0.150740	+	0.988573i	$0.548166\pi$
$284$		0			0
$285$	60.6466	−	35.0143i	0.212795	−	0.122857i
$286$		0			0
$287$	373.900	−	35.6811i	1.30279	−	0.124325i
$288$		0			0
$289$	−121.705	−	210.799i	−0.421125	−	0.729410i
$290$		0			0
$291$	−123.333	+	213.620i	−0.423826	+	0.734089i
$292$		0			0
$293$			138.398i			0.472347i	0.971711	+	0.236173i	$0.0758933\pi$
$293$			138.398i			0.472347i	−0.971711	+	0.236173i	$0.924107\pi$
$294$		0			0
$295$	382.302			1.29594
$296$		0			0
$297$	17.0216	+	9.82742i	0.0573118	+	0.0330890i
$298$		0			0
$299$	315.359	−	182.072i	1.05471	−	0.608938i
$300$		0			0
$301$	−27.9577	−	292.967i	−0.0928828	−	0.973312i
$302$		0			0
$303$	127.020	+	220.006i	0.419209	+	0.726092i
$304$		0			0
$305$	−366.459	+	634.725i	−1.20150	+	2.08107i
$306$		0			0
$307$		−	157.473i		−	0.512941i	−0.966552	−	0.256471i	$-0.917440\pi$
$307$		−	157.473i		−	0.512941i	0.966552	−	0.256471i	$-0.0825597\pi$
$308$		0			0
$309$	−13.3354			−0.0431567
$310$		0			0
$311$	−237.994	−	137.406i	−0.765253	−	0.441819i	0.0659254	−	0.997825i	$-0.479000\pi$
$311$	−237.994	−	137.406i	−0.765253	−	0.441819i	−0.831179	+	0.556005i	$0.812333\pi$
$312$		0			0
$313$	152.602	−	88.1048i	0.487546	−	0.281485i	−0.236010	−	0.971751i	$-0.575840\pi$
$313$	152.602	−	88.1048i	0.487546	−	0.281485i	0.723556	+	0.690266i	$0.242506\pi$
$314$		0			0
$315$	−53.4506	+	117.022i	−0.169685	+	0.371500i
$316$		0			0
$317$	146.183	+	253.197i	0.461146	+	0.798729i	0.999018	−	0.0442975i	$-0.0141050\pi$
$317$	146.183	+	253.197i	0.461146	+	0.798729i	−0.537872	+	0.843027i	$0.680772\pi$
$318$		0			0
$319$	−12.4315	+	21.5319i	−0.0389701	+	0.0674983i
$320$		0			0
$321$			241.784i			0.753221i
$322$		0			0
$323$	44.5608			0.137959
$324$		0			0
$325$	−100.852	−	58.2271i	−0.310315	−	0.179160i
$326$		0			0
$327$	227.418	−	131.300i	0.695467	−	0.401528i
$328$		0			0
$329$	−233.613	−	328.104i	−0.710070	−	0.997277i
$330$		0			0
$331$	−71.2984	−	123.492i	−0.215403	−	0.373089i	0.737994	−	0.674807i	$-0.235773\pi$
$331$	−71.2984	−	123.492i	−0.215403	−	0.373089i	−0.953397	+	0.301718i	$0.902440\pi$
$332$		0			0
$333$	100.600	−	174.245i	0.302103	−	0.523258i
$334$		0			0
$335$		−	341.527i		−	1.01948i
$336$		0			0
$337$	477.413			1.41666			0.708328	−	0.705884i	$-0.249450\pi$
$337$	477.413			1.41666			0.708328	+	0.705884i	$0.249450\pi$
$338$		0			0
$339$	−60.7213	−	35.0574i	−0.179119	−	0.103414i
$340$		0			0
$341$	−71.8466	+	41.4806i	−0.210694	+	0.121644i
$342$		0			0
$343$	−96.5767	−	329.123i	−0.281565	−	0.959542i
$344$		0			0
$345$	207.891	+	360.078i	0.602582	+	1.04370i
$346$		0			0
$347$	226.686	−	392.632i	0.653275	−	1.13151i	−0.329048	−	0.944313i	$-0.606728\pi$
$347$	226.686	−	392.632i	0.653275	−	1.13151i	0.982323	−	0.187192i	$-0.0599387\pi$
$348$		0			0
$349$			55.8211i			0.159946i	0.996797	+	0.0799730i	$0.0254834\pi$
$349$			55.8211i			0.159946i	−0.996797	+	0.0799730i	$0.974517\pi$
$350$		0			0
$351$	48.2889			0.137575
$352$		0			0
$353$	−197.638	−	114.107i	−0.559882	−	0.323248i	0.193216	−	0.981156i	$-0.438108\pi$
$353$	−197.638	−	114.107i	−0.559882	−	0.323248i	−0.753098	+	0.657908i	$0.771442\pi$
$354$		0			0
$355$	−695.859	+	401.754i	−1.96017	+	1.13170i
$356$		0			0
$357$	−66.6871	+	47.4818i	−0.186799	+	0.133002i
$358$		0			0
$359$	233.905	+	405.136i	0.651547	+	1.12851i	0.982748	+	0.184952i	$0.0592128\pi$
$359$	233.905	+	405.136i	0.651547	+	1.12851i	−0.331201	+	0.943560i	$0.607454\pi$
$360$		0			0
$361$	−158.722	+	274.915i	−0.439674	+	0.761539i
$362$		0			0
$363$			184.796i			0.509080i
$364$		0			0
$365$	471.983			1.29311
$366$		0			0
$367$	−264.699	−	152.824i	−0.721252	−	0.416415i	0.0939615	−	0.995576i	$-0.470047\pi$
$367$	−264.699	−	152.824i	−0.721252	−	0.416415i	−0.815213	+	0.579161i	$0.803380\pi$
$368$		0			0
$369$	139.405	−	80.4854i	0.377791	−	0.218118i
$370$		0			0
$371$	72.7257	+	33.2178i	0.196026	+	0.0895359i
$372$		0			0
$373$	−131.217	−	227.274i	−0.351787	−	0.609313i	0.634776	−	0.772697i	$-0.281093\pi$
$373$	−131.217	−	227.274i	−0.351787	−	0.609313i	−0.986563	+	0.163383i	$0.947759\pi$
$374$		0			0
$375$	−66.1536	+	114.581i	−0.176410	+	0.305550i
$376$		0			0
$377$			61.0843i			0.162027i
$378$		0			0
$379$	−489.503			−1.29156			−0.645782	−	0.763522i	$-0.723469\pi$
$379$	−489.503			−1.29156			−0.645782	+	0.763522i	$0.723469\pi$
$380$		0			0
$381$	−132.505	−	76.5019i	−0.347782	−	0.200792i
$382$		0			0
$383$	289.022	−	166.867i	0.754627	−	0.435684i	−0.0727364	−	0.997351i	$-0.523173\pi$
$383$	289.022	−	166.867i	0.754627	−	0.435684i	0.827363	+	0.561667i	$0.189840\pi$
$384$		0			0
$385$	161.478	−	15.4098i	0.419423	−	0.0400254i
$386$		0			0
$387$	−63.0639	−	109.230i	−0.162956	−	0.282248i
$388$		0			0
$389$	−298.042	+	516.223i	−0.766174	+	1.32705i	0.173449	+	0.984843i	$0.444509\pi$
$389$	−298.042	+	516.223i	−0.766174	+	1.32705i	−0.939624	+	0.342210i	$0.888825\pi$
$390$		0			0
$391$			264.571i			0.676653i
$392$		0			0
$393$	117.170			0.298142
$394$		0			0
$395$	−793.137	−	457.918i	−2.00794	−	1.15929i
$396$		0			0
$397$	268.394	−	154.957i	0.676055	−	0.390321i	−0.122312	−	0.992492i	$-0.539031\pi$
$397$	268.394	−	154.957i	0.676055	−	0.390321i	0.798367	+	0.602171i	$0.205697\pi$
$398$		0			0
$399$	7.60138	+	79.6543i	0.0190511	+	0.199635i
$400$		0			0
$401$	167.573	+	290.245i	0.417888	+	0.723803i	0.995727	−	0.0923475i	$-0.0294371\pi$
$401$	167.573	+	290.245i	0.417888	+	0.723803i	−0.577839	+	0.816151i	$0.696104\pi$
$402$		0			0
$403$	−101.911	+	176.516i	−0.252882	+	0.438004i
$404$		0			0
$405$			55.1364i			0.136139i
$406$		0			0
$407$	−253.685			−0.623306
$408$		0			0
$409$	−302.456	−	174.623i	−0.739501	−	0.426951i	0.0823869	−	0.996600i	$-0.473746\pi$
$409$	−302.456	−	174.623i	−0.739501	−	0.426951i	−0.821888	+	0.569649i	$0.807079\pi$
$410$		0			0
$411$	247.857	−	143.100i	0.603058	−	0.348176i
$412$		0			0
$413$	−181.488	+	397.341i	−0.439437	+	0.962085i
$414$		0			0
$415$	−121.805	−	210.973i	−0.293507	−	0.508369i
$416$		0			0
$417$	63.2727	−	109.591i	0.151733	−	0.262809i
$418$		0			0
$419$		−	359.369i		−	0.857683i	−0.903380	−	0.428841i	$-0.858922\pi$
$419$		−	359.369i		−	0.857683i	0.903380	−	0.428841i	$-0.141078\pi$
$420$		0			0
$421$	−831.803			−1.97578			−0.987890	−	0.155159i	$-0.950411\pi$
$421$	−831.803			−1.97578			−0.987890	+	0.155159i	$0.950411\pi$
$422$		0			0
$423$	−149.491	−	86.3088i	−0.353407	−	0.204040i
$424$		0			0
$425$	73.2748	−	42.3052i	0.172411	−	0.0995417i
$426$		0			0
$427$	−485.727	−	682.192i	−1.13753	−	1.59764i
$428$		0			0
$429$	−30.4427	−	52.7283i	−0.0709620	−	0.122910i
$430$		0			0
$431$	−161.420	+	279.587i	−0.374524	+	0.648694i	−0.990256	−	0.139262i	$-0.955527\pi$
$431$	−161.420	+	279.587i	−0.374524	+	0.648694i	0.615732	+	0.787956i	$0.288860\pi$
$432$		0			0
$433$			523.962i			1.21007i	0.796197	+	0.605037i	$0.206842\pi$
$433$			523.962i			1.21007i	−0.796197	+	0.605037i	$0.793158\pi$
$434$		0			0
$435$	−69.7463			−0.160336
$436$		0			0
$437$	223.954	+	129.300i	0.512481	+	0.295881i
$438$		0			0
$439$	606.881	−	350.383i	1.38242	−	0.798138i	0.389971	−	0.920827i	$-0.372485\pi$
$439$	606.881	−	350.383i	1.38242	−	0.798138i	0.992445	+	0.122689i	$0.0391516\pi$
$440$		0			0
$441$	−96.2516	−	111.106i	−0.218258	−	0.251942i
$442$		0			0
$443$	48.4446	+	83.9086i	0.109356	+	0.189410i	0.915509	−	0.402296i	$-0.131788\pi$
$443$	48.4446	+	83.9086i	0.109356	+	0.189410i	−0.806154	+	0.591706i	$0.798455\pi$
$444$		0			0
$445$	171.539	−	297.114i	0.385481	−	0.667672i
$446$		0			0
$447$		−	260.826i		−	0.583504i
$448$		0			0
$449$	−499.063			−1.11150			−0.555749	−	0.831350i	$-0.687568\pi$
$449$	−499.063			−1.11150			−0.555749	+	0.831350i	$0.687568\pi$
$450$		0			0
$451$	−175.770	−	101.481i	−0.389734	−	0.225013i
$452$		0			0
$453$	−208.476	+	120.364i	−0.460213	+	0.265704i
$454$		0			0
$455$	324.645	−	231.150i	0.713505	−	0.508022i
$456$		0			0
$457$	−158.284	−	274.156i	−0.346354	−	0.599903i	0.639245	−	0.769003i	$-0.279247\pi$
$457$	−158.284	−	274.156i	−0.346354	−	0.599903i	−0.985599	+	0.169100i	$0.945914\pi$
$458$		0			0
$459$	−17.5423	+	30.3841i	−0.0382184	+	0.0661963i
$460$		0			0
$461$		−	387.287i		−	0.840103i	−0.907500	−	0.420051i	$-0.862012\pi$
$461$		−	387.287i		−	0.840103i	0.907500	−	0.420051i	$-0.137988\pi$
$462$		0			0
$463$	909.661			1.96471			0.982355	−	0.187027i	$-0.0598852\pi$
$463$	909.661			1.96471			0.982355	+	0.187027i	$0.0598852\pi$
$464$		0			0
$465$	−201.546	−	116.363i	−0.433433	−	0.250243i
$466$		0			0
$467$	−38.4408	+	22.1938i	−0.0823143	+	0.0475242i	−0.540592	−	0.841285i	$-0.681800\pi$
$467$	−38.4408	+	22.1938i	−0.0823143	+	0.0475242i	0.458278	+	0.888809i	$0.348466\pi$
$468$		0			0
$469$	354.962	+	162.131i	0.756848	+	0.345694i
$470$		0			0
$471$	136.184	+	235.877i	0.289137	+	0.500800i
$472$		0			0
$473$	−79.5146	+	137.723i	−0.168107	+	0.291170i
$474$		0			0
$475$		−	82.7008i		−	0.174107i
$476$		0			0
$477$	34.2655			0.0718354
$478$		0			0
$479$	129.513	+	74.7741i	0.270381	+	0.156105i	0.629061	−	0.777356i	$-0.283440\pi$
$479$	129.513	+	74.7741i	0.270381	+	0.156105i	−0.358680	+	0.933461i	$0.616773\pi$
$480$		0			0
$481$	−539.764	+	311.633i	−1.12217	+	0.647885i
$482$		0			0
$483$	−472.932	+	45.1318i	−0.979156	+	0.0934405i
$484$		0			0
$485$	436.230	+	755.573i	0.899444	+	1.55788i
$486$		0			0
$487$	−28.5141	+	49.3879i	−0.0585505	+	0.101413i	−0.893815	−	0.448436i	$-0.851981\pi$
$487$	−28.5141	+	49.3879i	−0.0585505	+	0.101413i	0.835264	+	0.549848i	$0.185315\pi$
$488$		0			0
$489$			36.9319i			0.0755254i
$490$		0			0
$491$	−563.958			−1.14859			−0.574296	−	0.818648i	$-0.694724\pi$
$491$	−563.958			−1.14859			−0.574296	+	0.818648i	$0.694724\pi$
$492$		0			0
$493$	−38.4352	−	22.1906i	−0.0779619	−	0.0450113i
$494$		0			0
$495$	60.2054	−	34.7596i	0.121627	−	0.0702214i
$496$		0			0
$497$	−87.2182	−	913.954i	−0.175489	−	1.83894i
$498$		0			0
$499$	194.019	+	336.050i	0.388815	+	0.673447i	0.992290	−	0.123935i	$-0.0395513\pi$
$499$	194.019	+	336.050i	0.388815	+	0.673447i	−0.603476	+	0.797381i	$0.706218\pi$
$500$		0			0
$501$	154.125	−	266.951i	0.307634	−	0.532837i
$502$		0			0
$503$			712.944i			1.41738i	0.705518	+	0.708692i	$0.250714\pi$
$503$			712.944i			1.41738i	−0.705518	+	0.708692i	$0.749286\pi$
$504$		0			0
$505$	898.543			1.77929
$506$		0			0
$507$	123.955	+	71.5653i	0.244487	+	0.141155i
$508$		0			0
$509$	446.040	−	257.521i	0.876306	−	0.505935i	0.00686712	−	0.999976i	$-0.497814\pi$
$509$	446.040	−	257.521i	0.876306	−	0.505935i	0.869439	+	0.494041i	$0.164481\pi$
$510$		0			0
$511$	−224.061	+	490.550i	−0.438476	+	0.959980i
$512$		0			0
$513$	17.1463	+	29.6983i	0.0334236	+	0.0578914i
$514$		0			0
$515$	−23.5837	+	40.8482i	−0.0457936	+	0.0793169i
$516$		0			0
$517$			217.647i			0.420980i
$518$		0			0
$519$	190.702			0.367442
$520$		0			0
$521$	27.7063	+	15.9962i	0.0531791	+	0.0307030i	0.526354	−	0.850266i	$-0.323559\pi$
$521$	27.7063	+	15.9962i	0.0531791	+	0.0307030i	−0.473175	+	0.880969i	$0.656892\pi$
$522$		0			0
$523$	275.525	−	159.075i	0.526817	−	0.304158i	−0.212902	−	0.977073i	$-0.568292\pi$
$523$	275.525	−	159.075i	0.526817	−	0.304158i	0.739719	+	0.672916i	$0.234958\pi$
$524$		0			0
$525$	88.1219	+	123.765i	0.167851	+	0.235743i
$526$		0			0
$527$	−74.0443	−	128.248i	−0.140501	−	0.243356i
$528$		0			0
$529$	−503.194	+	871.557i	−0.951217	+	1.64756i
$530$		0			0
$531$			187.211i			0.352564i
$532$		0			0
$533$	−498.645			−0.935543
$534$		0			0
$535$	740.616	+	427.595i	1.38433	+	0.799243i
$536$		0			0
$537$	42.3674	−	24.4608i	0.0788964	−	0.0455509i
$538$		0			0
$539$	−60.6412	+	175.145i	−0.112507	+	0.324945i
$540$		0			0
$541$	−119.509	−	206.995i	−0.220903	−	0.382615i	0.734179	−	0.678956i	$-0.237567\pi$
$541$	−119.509	−	206.995i	−0.220903	−	0.382615i	−0.955082	+	0.296340i	$0.904234\pi$
$542$		0			0
$543$	−178.757	+	309.616i	−0.329202	+	0.570195i
$544$		0			0
$545$		−	928.814i		−	1.70425i
$546$		0			0
$547$	436.346			0.797707			0.398854	−	0.917015i	$-0.369408\pi$
$547$	436.346			0.797707			0.398854	+	0.917015i	$0.369408\pi$
$548$		0			0
$549$	−310.821	−	179.453i	−0.566159	−	0.326872i
$550$		0			0
$551$	−37.5677	+	21.6897i	−0.0681810	+	0.0393643i
$552$		0			0
$553$	852.451	−	606.953i	1.54150	−	1.09756i
$554$		0			0
$555$	−355.823	−	616.304i	−0.641123	−	1.11046i
$556$		0			0
$557$	442.789	−	766.932i	0.794953	−	1.37690i	−0.127917	−	0.991785i	$-0.540829\pi$
$557$	442.789	−	766.932i	0.794953	−	1.37690i	0.922869	−	0.385113i	$-0.125838\pi$
$558$		0			0
$559$			390.710i			0.698944i
$560$		0			0
$561$	44.2366			0.0788532
$562$		0			0
$563$	−154.219	−	89.0382i	−0.273923	−	0.158150i	0.356746	−	0.934201i	$-0.383886\pi$
$563$	−154.219	−	89.0382i	−0.273923	−	0.158150i	−0.630669	+	0.776052i	$0.717219\pi$
$564$		0			0
$565$	−214.771	+	123.998i	−0.380126	+	0.219466i
$566$		0			0
$567$	−57.3053	−	26.1745i	−0.101068	−	0.0461631i
$568$		0			0
$569$	−451.288	−	781.654i	−0.793125	−	1.37373i	−0.924023	−	0.382336i	$-0.875120\pi$
$569$	−451.288	−	781.654i	−0.793125	−	1.37373i	0.130898	−	0.991396i	$-0.458214\pi$
$570$		0			0
$571$	−40.0141	+	69.3064i	−0.0700771	+	0.121377i	−0.898935	−	0.438082i	$-0.855658\pi$
$571$	−40.0141	+	69.3064i	−0.0700771	+	0.121377i	0.828858	+	0.559459i	$0.188991\pi$
$572$		0			0
$573$			110.395i			0.192662i
$574$		0			0
$575$	491.020			0.853948
$576$		0			0
$577$	436.345	+	251.924i	0.756231	+	0.436610i	0.827941	−	0.560815i	$-0.189512\pi$
$577$	436.345	+	251.924i	0.756231	+	0.436610i	−0.0717099	+	0.997426i	$0.522846\pi$
$578$		0			0
$579$	101.028	−	58.3288i	0.174488	−	0.100741i
$580$		0			0
$581$	277.096	−	26.4431i	0.476929	−	0.0455131i
$582$		0			0
$583$	−21.6020	−	37.4157i	−0.0370531	−	0.0641779i
$584$		0			0
$585$	85.3989	−	147.915i	0.145981	−	0.252846i
$586$		0			0
$587$			458.274i			0.780706i	0.920665	+	0.390353i	$0.127647\pi$
$587$			458.274i			0.780706i	−0.920665	+	0.390353i	$0.872353\pi$
$588$		0			0
$589$	−144.746			−0.245749
$590$		0			0
$591$	144.106	+	83.1997i	0.243834	+	0.140778i
$592$		0			0
$593$	−580.642	+	335.234i	−0.979160	+	0.565318i	−0.902017	−	0.431701i	$-0.857913\pi$
$593$	−580.642	+	335.234i	−0.979160	+	0.565318i	−0.0771438	+	0.997020i	$0.524580\pi$
$594$		0			0
$595$	27.5069	+	288.243i	0.0462301	+	0.484442i
$596$		0			0
$597$	178.392	+	308.985i	0.298815	+	0.517562i
$598$		0			0
$599$	220.065	−	381.163i	0.367387	−	0.636332i	−0.621770	−	0.783200i	$-0.713586\pi$
$599$	220.065	−	381.163i	0.367387	−	0.636332i	0.989156	+	0.146868i	$0.0469193\pi$
$600$		0			0
$601$			732.160i			1.21824i	0.793080	+	0.609118i	$0.208476\pi$
$601$			732.160i			1.21824i	−0.793080	+	0.609118i	$0.791524\pi$
$602$		0			0
$603$	167.244			0.277353
$604$		0			0
$605$	566.055	+	326.812i	0.935628	+	0.540185i
$606$		0			0
$607$	−283.101	+	163.449i	−0.466394	+	0.269273i	−0.714729	−	0.699401i	$-0.753450\pi$
$607$	−283.101	+	163.449i	−0.466394	+	0.269273i	0.248335	+	0.968674i	$0.420117\pi$
$608$		0			0
$609$	33.1102	−	72.4899i	0.0543681	−	0.119031i
$610$		0			0
$611$	267.362	+	463.084i	0.437580	+	0.757911i
$612$		0			0
$613$	494.332	−	856.207i	0.806414	−	1.39675i	−0.108919	−	0.994051i	$-0.534739\pi$
$613$	494.332	−	856.207i	0.806414	−	1.39675i	0.915333	−	0.402699i	$-0.131928\pi$
$614$		0			0
$615$		−	569.354i		−	0.925779i
$616$		0			0
$617$	280.536			0.454678			0.227339	−	0.973816i	$-0.426997\pi$
$617$	280.536			0.454678			0.227339	+	0.973816i	$0.426997\pi$
$618$		0			0
$619$	894.439	+	516.405i	1.44497	+	0.834256i	0.998176	−	0.0603780i	$-0.0192306\pi$
$619$	894.439	+	516.405i	1.44497	+	0.834256i	0.446799	+	0.894634i	$0.352564\pi$
$620$		0			0
$621$	−176.328	+	101.803i	−0.283942	+	0.163934i
$622$		0			0
$623$	227.368	+	319.334i	0.364957	+	0.512574i
$624$		0			0
$625$	390.625	+	676.582i	0.624999	+	1.08253i
$626$		0			0
$627$	21.6191	−	37.4454i	0.0344802	−	0.0597215i
$628$		0			0
$629$		−	452.837i		−	0.719931i
$630$		0			0
$631$	178.252			0.282491			0.141245	−	0.989975i	$-0.454889\pi$
$631$	178.252			0.282491			0.141245	+	0.989975i	$0.454889\pi$
$632$		0			0
$633$	−182.913	−	105.605i	−0.288963	−	0.166833i
$634$		0			0
$635$	−468.671	+	270.587i	−0.738064	+	0.426122i
$636$		0			0
$637$	86.1265	+	447.148i	0.135207	+	0.701958i
$638$		0			0
$639$	−196.737	−	340.758i	−0.307883	−	0.533268i
$640$		0			0
$641$	−334.263	+	578.961i	−0.521471	+	0.903215i	0.478217	+	0.878242i	$0.341283\pi$
$641$	−334.263	+	578.961i	−0.521471	+	0.903215i	−0.999688	+	0.0249729i	$0.992050\pi$
$642$		0			0
$643$		−	313.584i		−	0.487690i	−0.969814	−	0.243845i	$-0.921591\pi$
$643$		−	313.584i		−	0.487690i	0.969814	−	0.243845i	$-0.0784088\pi$
$644$		0			0
$645$	−446.114			−0.691649
$646$		0			0
$647$	−292.310	−	168.765i	−0.451793	−	0.260843i	0.256794	−	0.966466i	$-0.417334\pi$
$647$	−292.310	−	168.765i	−0.451793	−	0.260843i	−0.708587	+	0.705623i	$0.750667\pi$
$648$		0			0
$649$	204.423	−	118.024i	0.314981	−	0.181855i
$650$		0			0
$651$	216.619	−	154.234i	0.332748	−	0.236919i
$652$		0			0
$653$	−451.677	−	782.328i	−0.691695	−	1.19805i	−0.971282	−	0.237931i	$-0.923531\pi$
$653$	−451.677	−	782.328i	−0.691695	−	1.19805i	0.279587	−	0.960120i	$-0.409803\pi$
$654$		0			0
$655$	207.215	−	358.907i	0.316358	−	0.547949i
$656$		0			0
$657$			231.128i			0.351793i
$658$		0			0
$659$	768.092			1.16554			0.582771	−	0.812637i	$-0.301969\pi$
$659$	768.092			1.16554			0.582771	+	0.812637i	$0.301969\pi$
$660$		0			0
$661$	356.130	+	205.612i	0.538774	+	0.311062i	0.744582	−	0.667531i	$-0.232649\pi$
$661$	356.130	+	205.612i	0.538774	+	0.311062i	−0.205808	+	0.978592i	$0.565982\pi$
$662$		0			0
$663$	94.1217	−	54.3412i	0.141963	−	0.0819626i
$664$		0			0
$665$	257.435	+	117.585i	0.387120	+	0.176819i
$666$		0			0
$667$	−128.779	−	223.051i	−0.193071	−	0.334410i
$668$		0			0
$669$	16.0237	−	27.7539i	0.0239517	−	0.0414856i
$670$		0			0
$671$			452.529i			0.674410i
$672$		0			0
$673$	−818.448			−1.21612			−0.608060	−	0.793891i	$-0.708052\pi$
$673$	−818.448			−1.21612			−0.608060	+	0.793891i	$0.708052\pi$
$674$		0			0
$675$	56.3901	+	32.5568i	0.0835409	+	0.0482323i
$676$		0			0
$677$	−48.0858	+	27.7623i	−0.0710277	+	0.0410079i	−0.535093	−	0.844793i	$-0.679724\pi$
$677$	−48.0858	+	27.7623i	−0.0710277	+	0.0410079i	0.464066	+	0.885801i	$0.346390\pi$
$678$		0			0
$679$	−992.384	+	94.7028i	−1.46154	+	0.139474i
$680$		0			0
$681$	−127.348	−	220.573i	−0.187001	−	0.323896i
$682$		0			0
$683$	−38.1419	+	66.0637i	−0.0558447	+	0.0967258i	−0.892596	−	0.450857i	$-0.851118\pi$
$683$	−38.1419	+	66.0637i	−0.0558447	+	0.0967258i	0.836752	+	0.547583i	$0.184452\pi$
$684$		0			0
$685$		−	1012.29i		−	1.47780i
$686$		0			0
$687$	−623.391			−0.907410
$688$		0			0
$689$	−91.9245	−	53.0726i	−0.133417	−	0.0770285i
$690$		0			0
$691$	−19.4780	+	11.2456i	−0.0281881	+	0.0162744i	−0.514028	−	0.857774i	$-0.671847\pi$
$691$	−19.4780	+	11.2456i	−0.0281881	+	0.0162744i	0.485840	+	0.874048i	$0.338514\pi$
$692$		0			0
$693$	7.54608	+	79.0749i	0.0108890	+	0.114105i
$694$		0			0
$695$	−223.796	−	387.625i	−0.322008	−	0.557734i
$696$		0			0
$697$	181.146	−	313.755i	0.259894	−	0.450150i
$698$		0			0
$699$		−	76.3282i		−	0.109196i
$700$		0			0
$701$	−854.197			−1.21854			−0.609270	−	0.792963i	$-0.708538\pi$
$701$	−854.197			−1.21854			−0.609270	+	0.792963i	$0.708538\pi$
$702$		0			0
$703$	−383.317	−	221.308i	−0.545258	−	0.314805i
$704$		0			0
$705$	−528.751	+	305.274i	−0.750001	+	0.433013i
$706$		0			0
$707$	−426.558	+	933.889i	−0.603336	+	1.32092i
$708$		0			0
$709$	79.3009	+	137.353i	0.111849	+	0.193728i	0.916516	−	0.399999i	$-0.130989\pi$
$709$	79.3009	+	137.353i	0.111849	+	0.193728i	−0.804667	+	0.593727i	$0.797656\pi$
$710$		0			0
$711$	224.240	−	388.395i	0.315387	−	0.546266i
$712$		0			0
$713$		−	859.403i		−	1.20533i
$714$		0			0
$715$	−215.352			−0.301191
$716$		0			0
$717$	247.615	+	142.961i	0.345349	+	0.199387i
$718$		0			0
$719$	−329.191	+	190.059i	−0.457846	+	0.264338i	−0.711138	−	0.703052i	$-0.751820\pi$
$719$	−329.191	+	190.059i	−0.457846	+	0.264338i	0.253292	+	0.967390i	$0.418487\pi$
$720$		0			0
$721$	−31.2593	−	43.9030i	−0.0433555	−	0.0608918i
$722$		0			0
$723$	−115.828	−	200.620i	−0.160204	−	0.277482i
$724$		0			0
$725$	−41.1837	+	71.3322i	−0.0568051	+	0.0983893i
$726$		0			0
$727$		−	159.283i		−	0.219096i	−0.993981	−	0.109548i	$-0.965060\pi$
$727$		−	159.283i		−	0.219096i	0.993981	−	0.109548i	$-0.0349404\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−245.841	−	141.936i	−0.336307	−	0.194167i
$732$		0			0
$733$	−154.308	+	89.0895i	−0.210515	+	0.121541i	−0.601551	−	0.798835i	$-0.705450\pi$
$733$	−154.308	+	89.0895i	−0.210515	+	0.121541i	0.391036	+	0.920376i	$0.372117\pi$
$734$		0			0
$735$	−510.555	+	98.3396i	−0.694632	+	0.133795i
$736$		0			0
$737$	−105.436	−	182.620i	−0.143060	−	0.247788i
$738$		0			0
$739$	−158.693	+	274.864i	−0.214740	+	0.371941i	−0.953192	−	0.302365i	$-0.902224\pi$
$739$	−158.693	+	274.864i	−0.214740	+	0.371941i	0.738452	+	0.674306i	$0.235557\pi$
$740$		0			0
$741$		−	106.229i		−	0.143360i
$742$		0			0
$743$	−1055.73			−1.42090			−0.710450	−	0.703748i	$-0.751508\pi$
$743$	−1055.73			−1.42090			−0.710450	+	0.703748i	$0.751508\pi$
$744$		0			0
$745$	−798.945	−	461.271i	−1.07241	−	0.619156i
$746$		0			0
$747$	103.312	−	59.6474i	0.138303	−	0.0798493i
$748$		0			0
$749$	−796.003	+	566.761i	−1.06275	+	0.756690i
$750$		0			0
$751$	−153.605	−	266.051i	−0.204533	−	0.354262i	0.745451	−	0.666561i	$-0.232234\pi$
$751$	−153.605	−	266.051i	−0.204533	−	0.354262i	−0.949984	+	0.312299i	$0.898901\pi$
$752$		0			0
$753$	−349.562	+	605.459i	−0.464226	+	0.804062i
$754$		0			0
$755$			851.454i			1.12775i
$756$		0			0
$757$	−711.179			−0.939470			−0.469735	−	0.882808i	$-0.655651\pi$
$757$	−711.179			−0.939470			−0.469735	+	0.882808i	$0.655651\pi$
$758$		0			0
$759$	222.325	+	128.359i	0.292918	+	0.169116i
$760$		0			0
$761$	457.221	−	263.977i	0.600816	−	0.346881i	−0.168546	−	0.985694i	$-0.553907\pi$
$761$	457.221	−	263.977i	0.600816	−	0.346881i	0.769363	+	0.638812i	$0.220574\pi$
$762$		0			0
$763$	965.350	+	440.929i	1.26520	+	0.577888i
$764$		0			0
$765$	62.0470	+	107.469i	0.0811072	+	0.140482i
$766$		0			0
$767$	289.965	−	502.235i	0.378051	−	0.654804i
$768$		0			0
$769$		−	831.961i		−	1.08187i	−0.841063	−	0.540937i	$-0.818070\pi$
$769$		−	831.961i		−	1.08187i	0.841063	−	0.540937i	$-0.181930\pi$
$770$		0			0
$771$	484.836			0.628840
$772$		0			0
$773$	657.060	+	379.354i	0.850012	+	0.490755i	0.860655	−	0.509188i	$-0.170054\pi$
$773$	657.060	+	379.354i	0.850012	+	0.490755i	−0.0106426	+	0.999943i	$0.503388\pi$
$774$		0			0
$775$	−238.017	+	137.419i	−0.307119	+	0.177315i
$776$		0			0
$777$	809.465	−	77.2469i	1.04178	−	0.0994169i
$778$		0			0
$779$	−177.058	−	306.673i	−0.227289	−	0.393676i
$780$		0			0
$781$	−248.058	+	429.648i	−0.317615	+	0.550126i
$782$		0			0
$783$		−	34.1544i		−	0.0436199i
$784$		0			0
$785$	963.363			1.22721
$786$		0			0
$787$	−595.121	−	343.593i	−0.756190	−	0.436586i	0.0717363	−	0.997424i	$-0.477146\pi$
$787$	−595.121	−	343.593i	−0.756190	−	0.436586i	−0.827926	+	0.560837i	$0.810479\pi$
$788$		0			0
$789$	212.839	−	122.882i	0.269758	−	0.155745i
$790$		0			0
$791$	−26.9192	−	282.084i	−0.0340319	−	0.356617i
$792$		0			0
$793$	555.897	+	962.841i	0.701005	+	1.21418i
$794$		0			0
$795$	60.5985	−	104.960i	0.0762245	−	0.132025i
$796$		0			0
$797$		−	716.069i		−	0.898456i	−0.893417	−	0.449228i	$-0.851699\pi$
$797$		−	716.069i		−	0.898456i	0.893417	−	0.449228i	$-0.148301\pi$
$798$		0			0
$799$	−388.506			−0.486240
$800$		0			0
$801$	145.495	+	84.0017i	0.181642	+	0.104871i
$802$		0			0
$803$	252.377	−	145.710i	0.314292	−	0.181457i
$804$		0			0
$805$	−698.137	+	1528.47i	−0.867251	+	1.89872i
$806$		0			0
$807$	344.508	+	596.705i	0.426899	+	0.739411i
$808$		0			0
$809$	68.0836	−	117.924i	0.0841577	−	0.145765i	−0.820874	−	0.571109i	$-0.806513\pi$
$809$	68.0836	−	117.924i	0.0841577	−	0.145765i	0.905032	+	0.425344i	$0.139847\pi$
$810$		0			0
$811$		−	421.599i		−	0.519851i	−0.965629	−	0.259926i	$-0.916302\pi$
$811$		−	421.599i		−	0.519851i	0.965629	−	0.259926i	$-0.0836981\pi$
$812$		0			0
$813$	−757.124			−0.931272
$814$		0			0
$815$	113.127	+	65.3141i	0.138807	+	0.0801401i
$816$		0			0
$817$	−240.292	+	138.733i	−0.294115	+	0.169807i
$818$		0			0
$819$	113.193	+	158.977i	0.138209	+	0.194111i
$820$		0			0
$821$	−39.8238	−	68.9769i	−0.0485065	−	0.0840157i	0.840753	−	0.541419i	$-0.182113\pi$
$821$	−39.8238	−	68.9769i	−0.0485065	−	0.0840157i	−0.889259	+	0.457404i	$0.848779\pi$
$822$		0			0
$823$	666.149	−	1153.80i	0.809416	−	1.40195i	−0.103853	−	0.994593i	$-0.533117\pi$
$823$	666.149	−	1153.80i	0.809416	−	1.40195i	0.913269	−	0.407357i	$-0.133549\pi$
$824$		0			0
$825$		−	82.0991i		−	0.0995141i
$826$		0			0
$827$	468.548			0.566564			0.283282	−	0.959037i	$-0.408577\pi$
$827$	468.548			0.566564			0.283282	+	0.959037i	$0.408577\pi$
$828$		0			0
$829$	426.112	+	246.016i	0.514007	+	0.296762i	0.734479	−	0.678631i	$-0.237426\pi$
$829$	426.112	+	246.016i	0.514007	+	0.296762i	−0.220472	+	0.975393i	$0.570760\pi$
$830$		0			0
$831$	−7.96211	+	4.59692i	−0.00958136	+	0.00553180i
$832$		0			0
$833$	−312.640	−	108.247i	−0.375318	−	0.129948i
$834$		0			0
$835$	−545.139	−	944.208i	−0.652861	−	1.13079i
$836$		0			0
$837$	56.9823	−	98.6962i	0.0680792	−	0.117917i
$838$		0			0
$839$			1045.41i			1.24602i	0.782214	+	0.623010i	$0.214090\pi$
$839$			1045.41i			1.24602i	−0.782214	+	0.623010i	$0.785910\pi$
$840$		0			0
$841$	−797.795			−0.948627
$842$		0			0
$843$	446.493	+	257.783i	0.529648	+	0.305792i
$844$		0			0
$845$	438.428	−	253.127i	0.518850	−	0.299558i
$846$		0			0
$847$	−608.387	+	433.177i	−0.718285	+	0.511425i
$848$		0			0
$849$	178.296	+	308.817i	0.210007	+	0.363742i
$850$		0			0
$851$	1313.97	−	2275.87i	1.54404	−	2.67435i
$852$		0			0
$853$		−	339.686i		−	0.398225i	−0.979977	−	0.199113i	$-0.936194\pi$
$853$		−	339.686i		−	0.398225i	0.979977	−	0.199113i	$-0.0638060\pi$
$854$		0			0
$855$	121.293			0.141863
$856$		0			0
$857$	1216.76	+	702.497i	1.41979	+	0.819717i	0.996280	−	0.0861737i	$-0.0274640\pi$
$857$	1216.76	+	702.497i	1.41979	+	0.819717i	0.423511	+	0.905891i	$0.360797\pi$
$858$		0			0
$859$	1047.21	−	604.609i	1.21911	−	0.703853i	0.254381	−	0.967104i	$-0.418128\pi$
$859$	1047.21	−	604.609i	1.21911	−	0.703853i	0.964727	+	0.263251i	$0.0847949\pi$
$860$		0			0
$861$	591.751	+	270.285i	0.687283	+	0.313920i
$862$		0			0
$863$	−497.129	−	861.052i	−0.576047	−	0.997743i	−0.995927	−	0.0901632i	$-0.971261\pi$
$863$	−497.129	−	861.052i	−0.576047	−	0.997743i	0.419880	−	0.907580i	$-0.362072\pi$
$864$		0			0
$865$	337.257	−	584.146i	0.389893	−	0.675314i
$866$		0			0
$867$		−	421.599i		−	0.486273i
$868$		0			0
$869$	−565.470			−0.650713
$870$		0			0
$871$	−448.668	−	259.038i	−0.515118	−	0.297403i
$872$		0			0
$873$	−370.000	+	213.620i	−0.423826	+	0.244696i
$874$		0			0
$875$	−532.295	+	50.7967i	−0.608337	+	0.0580534i
$876$		0			0
$877$	777.369	+	1346.44i	0.886396	+	1.53528i	0.844105	+	0.536177i	$0.180132\pi$
$877$	777.369	+	1346.44i	0.886396	+	1.53528i	0.0422903	+	0.999105i	$0.486535\pi$
$878$		0			0
$879$	−119.856	+	207.596i	−0.136355	+	0.236173i
$880$		0			0
$881$			921.015i			1.04542i	0.852511	+	0.522710i	$0.175079\pi$
$881$			921.015i			1.04542i	−0.852511	+	0.522710i	$0.824921\pi$
$882$		0			0
$883$	−156.823			−0.177603			−0.0888014	−	0.996049i	$-0.528304\pi$
$883$	−156.823			−0.177603			−0.0888014	+	0.996049i	$0.528304\pi$
$884$		0			0
$885$	573.454	+	331.084i	0.647970	+	0.374106i
$886$		0			0
$887$	−1401.86	+	809.362i	−1.58045	+	0.912471i	−0.585653	+	0.810562i	$0.699162\pi$
$887$	−1401.86	+	809.362i	−1.58045	+	0.912471i	−0.994794	+	0.101909i	$0.967505\pi$
$888$		0			0
$889$	−58.7427	−	615.561i	−0.0660773	−	0.692419i
$890$		0			0
$891$	17.0216	+	29.4823i	0.0191039	+	0.0330890i
$892$		0			0
$893$	−189.869	+	328.862i	−0.212619	+	0.368267i
$894$		0			0
$895$		−	173.036i		−	0.193336i
$896$		0			0
$897$	630.717			0.703141
$898$		0			0
$899$	124.848	+	72.0813i	0.138875	+	0.0801794i
$900$		0			0
$901$	66.7882	−	38.5602i	0.0741267	−	0.0427971i
$902$		0			0
$903$	211.780	−	463.663i	0.234530	−	0.513469i
$904$		0			0
$905$	632.263	+	1095.11i	0.698633	+	1.21007i
$906$		0			0
$907$	279.345	−	483.839i	0.307988	−	0.533450i	−0.669934	−	0.742420i	$-0.733678\pi$
$907$	279.345	−	483.839i	0.307988	−	0.533450i	0.977922	+	0.208970i	$0.0670111\pi$
$908$		0			0
$909$			440.012i			0.484061i
$910$		0			0
$911$	510.774			0.560674			0.280337	−	0.959902i	$-0.409554\pi$
$911$	510.774			0.560674			0.280337	+	0.959902i	$0.409554\pi$
$912$		0			0
$913$	−130.262	−	75.2070i	−0.142675	−	0.0823735i
$914$		0			0
$915$	−1099.38	+	634.725i	−1.20150	+	0.693688i
$916$		0			0
$917$	274.655	+	385.747i	0.299515	+	0.420662i
$918$		0			0
$919$	−333.677	−	577.945i	−0.363087	−	0.628885i	0.625380	−	0.780320i	$-0.284944\pi$
$919$	−333.677	−	577.945i	−0.363087	−	0.628885i	−0.988467	+	0.151435i	$0.951611\pi$
$920$		0			0
$921$	136.376	−	236.209i	0.148073	−	0.256471i
$922$		0			0
$923$			1218.88i			1.32056i
$924$		0			0
$925$	−840.424			−0.908566
$926$		0			0
$927$	−20.0032	−	11.5488i	−0.0215784	−	0.0124583i
$928$		0			0
$929$	760.086	−	438.836i	0.818177	−	0.472375i	−0.0316106	−	0.999500i	$-0.510064\pi$
$929$	760.086	−	438.836i	0.818177	−	0.472375i	0.849787	+	0.527126i	$0.176730\pi$
$930$		0			0
$931$	−244.420	+	211.741i	−0.262535	+	0.227434i
$932$		0			0
$933$	−237.994	−	412.217i	−0.255084	−	0.441819i
$934$		0			0
$935$	78.2325	−	135.503i	0.0836711	−	0.144923i
$936$		0			0
$937$		−	211.107i		−	0.225301i	−0.993635	−	0.112650i	$-0.964066\pi$
$937$		−	211.107i		−	0.225301i	0.993635	−	0.112650i	$-0.0359340\pi$
$938$		0			0
$939$	305.204			0.325031
$940$		0			0
$941$	1321.72	+	763.093i	1.40459	+	0.810938i	0.994859	−	0.101270i	$-0.0322908\pi$
$941$	1321.72	+	763.093i	1.40459	+	0.810938i	0.409727	+	0.912208i	$0.365624\pi$
$942$		0			0
$943$	1820.81	−	1051.25i	1.93087	−	1.11479i
$944$		0			0
$945$	−181.520	+	129.244i	−0.192085	+	0.136766i
$946$		0			0
$947$	321.155	+	556.256i	0.339129	+	0.587388i	0.984269	−	0.176676i	$-0.0565345\pi$
$947$	321.155	+	556.256i	0.339129	+	0.587388i	−0.645140	+	0.764064i	$0.723201\pi$
$948$		0			0
$949$	357.986	−	620.050i	0.377224	−	0.653372i
$950$		0			0
$951$			506.394i			0.532486i
$952$		0			0
$953$	208.041			0.218302			0.109151	−	0.994025i	$-0.465187\pi$
$953$	208.041			0.218302			0.109151	+	0.994025i	$0.465187\pi$
$954$		0			0
$955$	338.156	+	195.234i	0.354090	+	0.204434i
$956$		0			0
$957$	−37.2944	+	21.5319i	−0.0389701	+	0.0224994i
$958$		0			0
$959$	1052.11	+	480.558i	1.09709	+	0.501103i
$960$		0			0
$961$	−239.983	−	415.663i	−0.249722	−	0.432532i
$962$		0			0
$963$	−209.391	+	362.676i	−0.217436	+	0.376610i
$964$		0			0
$965$		−	412.618i		−	0.427584i
$966$		0			0
$967$	−1485.38			−1.53607			−0.768034	−	0.640409i	$-0.778765\pi$
$967$	−1485.38			−1.53607			−0.768034	+	0.640409i	$0.778765\pi$
$968$		0			0
$969$	66.8412	+	38.5908i	0.0689795	+	0.0398254i
$970$		0			0
$971$	296.922	−	171.428i	0.305790	−	0.176548i	−0.339251	−	0.940696i	$-0.610174\pi$
$971$	296.922	−	171.428i	0.305790	−	0.176548i	0.645041	+	0.764148i	$0.276840\pi$
$972$		0			0
$973$	509.114	−	48.5845i	0.523241	−	0.0499327i
$974$		0			0
$975$	−100.852	−	174.681i	−0.103438	−	0.179160i
$976$		0			0
$977$	−835.089	+	1446.42i	−0.854748	+	1.48047i	0.0221298	+	0.999755i	$0.492955\pi$
$977$	−835.089	+	1446.42i	−0.854748	+	1.48047i	−0.876878	+	0.480713i	$0.840378\pi$
$978$		0			0
$979$		−	211.829i		−	0.216372i
$980$		0			0
$981$	454.835			0.463644
$982$		0			0
$983$	697.316	+	402.596i	0.709376	+	0.409558i	0.810830	−	0.585282i	$-0.199016\pi$
$983$	697.316	+	402.596i	0.709376	+	0.409558i	−0.101454	+	0.994840i	$0.532350\pi$
$984$		0			0
$985$	509.703	−	294.277i	0.517465	−	0.298759i
$986$		0			0
$987$	−66.2731	−	694.471i	−0.0671460	−	0.703618i
$988$		0			0
$989$	−823.698	−	1426.69i	−0.832860	−	1.44256i
$990$		0			0
$991$	−751.501	+	1301.64i	−0.758326	+	1.31346i	0.185378	+	0.982667i	$0.440649\pi$
$991$	−751.501	+	1301.64i	−0.758326	+	1.31346i	−0.943704	+	0.330792i	$0.892684\pi$
$992$		0			0
$993$		−	246.985i		−	0.248726i
$994$		0			0
$995$	1261.95			1.26829
$996$		0			0
$997$	609.714	+	352.019i	0.611549	+	0.353078i	0.773571	−	0.633709i	$-0.218468\pi$
$997$	609.714	+	352.019i	0.611549	+	0.353078i	−0.162023	+	0.986787i	$0.551802\pi$
$998$		0			0
$999$	301.801	−	174.245i	0.302103	−	0.174419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.z.b.73.4	✓	8
3.2	odd	2		504.3.by.c.73.1		8
4.3	odd	2		336.3.bh.g.241.4		8
7.2	even	3		1176.3.z.c.313.1		8
7.3	odd	6		1176.3.f.c.97.5		8
7.4	even	3		1176.3.f.c.97.4		8
7.5	odd	6	inner	168.3.z.b.145.4	yes	8
7.6	odd	2		1176.3.z.c.913.1		8
12.11	even	2		1008.3.cg.p.577.1		8
21.5	even	6		504.3.by.c.145.1		8
21.11	odd	6		3528.3.f.b.2449.2		8
21.17	even	6		3528.3.f.b.2449.7		8
28.3	even	6		2352.3.f.g.97.1		8
28.11	odd	6		2352.3.f.g.97.8		8
28.19	even	6		336.3.bh.g.145.4		8
84.47	odd	6		1008.3.cg.p.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.b.73.4	✓	8	1.1	even	1	trivial
168.3.z.b.145.4	yes	8	7.5	odd	6	inner
336.3.bh.g.145.4		8	28.19	even	6
336.3.bh.g.241.4		8	4.3	odd	2
504.3.by.c.73.1		8	3.2	odd	2
504.3.by.c.145.1		8	21.5	even	6
1008.3.cg.p.145.1		8	84.47	odd	6
1008.3.cg.p.577.1		8	12.11	even	2
1176.3.f.c.97.4		8	7.4	even	3
1176.3.f.c.97.5		8	7.3	odd	6
1176.3.z.c.313.1		8	7.2	even	3
1176.3.z.c.913.1		8	7.6	odd	2
2352.3.f.g.97.1		8	28.3	even	6
2352.3.f.g.97.8		8	28.11	odd	6
3528.3.f.b.2449.2		8	21.11	odd	6
3528.3.f.b.2449.7		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(5.30550 - 3.06313i) q^{5} +(0.664986 + 6.96834i) q^{7} +(1.50000 + 2.59808i) q^{9} +(1.89129 - 3.27581i) q^{11} -9.29319i q^{13} +10.6110 q^{15} +(5.84742 + 3.37601i) q^{17} +(5.71544 - 3.29981i) q^{19} +(-5.03728 + 11.0284i) q^{21} +(19.5920 + 33.9344i) q^{23} +(6.26557 - 10.8523i) q^{25} +5.19615i q^{27} -6.57302 q^{29} +(-18.9941 - 10.9662i) q^{31} +(5.67386 - 3.27581i) q^{33} +(24.8730 + 34.9336i) q^{35} +(-33.5334 - 58.0816i) q^{37} +(8.04814 - 13.9398i) q^{39} -53.6570i q^{41} -42.0426 q^{43} +(15.9165 + 9.18940i) q^{45} +(-49.8304 + 28.7696i) q^{47} +(-48.1156 + 9.26770i) q^{49} +(5.84742 + 10.1280i) q^{51} +(5.71091 - 9.89159i) q^{53} -23.1731i q^{55} +11.4309 q^{57} +(54.0433 + 31.2019i) q^{59} +(-103.607 + 59.8176i) q^{61} +(-17.1068 + 12.1802i) q^{63} +(-28.4663 - 49.3051i) q^{65} +(27.8740 - 48.2792i) q^{67} +67.8687i q^{69} -131.158 q^{71} +(66.7208 + 38.5213i) q^{73} +(18.7967 - 10.8523i) q^{75} +(24.0846 + 11.0008i) q^{77} +(-74.7467 - 129.465i) q^{79} +(-4.50000 + 7.79423i) q^{81} -39.7649i q^{83} +41.3647 q^{85} +(-9.85953 - 5.69240i) q^{87} +(48.4984 - 28.0006i) q^{89} +(64.7582 - 6.17984i) q^{91} +(-18.9941 - 32.8987i) q^{93} +(20.2155 - 35.0143i) q^{95} +142.413i q^{97} +11.3477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 6 q^{5} + 8 q^{7} + 12 q^{9} - 22 q^{11} - 12 q^{15} + 36 q^{17} + 42 q^{19} + 6 q^{21} + 48 q^{23} + 42 q^{25} + 68 q^{29} - 60 q^{31} - 66 q^{33} - 12 q^{35} - 118 q^{37} - 18 q^{39}+ \cdots - 132 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 6 * q^5 + 8 * q^7 + 12 * q^9 - 22 * q^11 - 12 * q^15 + 36 * q^17 + 42 * q^19 + 6 * q^21 + 48 * q^23 + 42 * q^25 + 68 * q^29 - 60 * q^31 - 66 * q^33 - 12 * q^35 - 118 * q^37 - 18 * q^39 - 92 * q^43 - 18 * q^45 - 12 * q^47 - 20 * q^49 + 36 * q^51 + 10 * q^53 + 84 * q^57 - 54 * q^59 + 24 * q^61 - 6 * q^63 - 148 * q^65 + 22 * q^67 - 392 * q^71 - 138 * q^73 + 126 * q^75 - 126 * q^77 + 164 * q^79 - 36 * q^81 + 200 * q^85 + 102 * q^87 - 60 * q^89 + 90 * q^91 - 60 * q^93 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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