LMFDB - Embedded newform 216.3.p.b.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827034 - 1.82099i) q^{2} +(-2.63203 + 3.01205i) q^{4} +(-3.84571 + 2.22032i) q^{5} +(0.704321 + 0.406640i) q^{7} +(7.66169 + 2.30184i) q^{8} +O(q^{10})$	\(q+(-0.827034 - 1.82099i) q^{2} +(-2.63203 + 3.01205i) q^{4} +(-3.84571 + 2.22032i) q^{5} +(0.704321 + 0.406640i) q^{7} +(7.66169 + 2.30184i) q^{8} +(7.22371 + 5.16672i) q^{10} +(3.72022 - 6.44360i) q^{11} +(18.0943 - 10.4468i) q^{13} +(0.157991 - 1.61887i) q^{14} +(-2.14484 - 15.8556i) q^{16} -1.74716 q^{17} +31.7920 q^{19} +(3.43431 - 17.4274i) q^{20} +(-14.8105 - 1.44541i) q^{22} +(6.44927 - 3.72348i) q^{23} +(-2.64036 + 4.57325i) q^{25} +(-33.9881 - 24.3098i) q^{26} +(-3.07861 + 1.05116i) q^{28} +(26.9672 + 15.5695i) q^{29} +(-4.91458 + 2.83744i) q^{31} +(-27.0991 + 17.0188i) q^{32} +(1.44496 + 3.18156i) q^{34} -3.61148 q^{35} -62.0787i q^{37} +(-26.2930 - 57.8930i) q^{38} +(-34.5754 + 8.15919i) q^{40} +(-2.74032 - 4.74637i) q^{41} +(-22.3782 + 38.7602i) q^{43} +(9.61671 + 28.1652i) q^{44} +(-12.1142 - 8.66462i) q^{46} +(71.1253 + 41.0642i) q^{47} +(-24.1693 - 41.8624i) q^{49} +(10.5115 + 1.02586i) q^{50} +(-16.1587 + 81.9972i) q^{52} -85.0348i q^{53} +33.0403i q^{55} +(4.46027 + 4.73679i) q^{56} +(6.04919 - 61.9836i) q^{58} +(21.8641 + 37.8697i) q^{59} +(61.1107 + 35.2823i) q^{61} +(9.23148 + 6.60276i) q^{62} +(53.4030 + 35.2720i) q^{64} +(-46.3903 + 80.3504i) q^{65} +(9.91758 + 17.1778i) q^{67} +(4.59857 - 5.26251i) q^{68} +(2.98682 + 6.57649i) q^{70} +69.3125i q^{71} -21.7177 q^{73} +(-113.045 + 51.3412i) q^{74} +(-83.6774 + 95.7589i) q^{76} +(5.24046 - 3.02558i) q^{77} +(-37.1475 - 21.4471i) q^{79} +(43.4529 + 56.2137i) q^{80} +(-6.37677 + 8.91551i) q^{82} +(3.53270 - 6.11881i) q^{83} +(6.71905 - 3.87924i) q^{85} +(89.0897 + 8.69457i) q^{86} +(43.3353 - 40.8055i) q^{88} -37.1192 q^{89} +16.9923 q^{91} +(-5.75935 + 29.2258i) q^{92} +(15.9546 - 163.480i) q^{94} +(-122.263 + 70.5883i) q^{95} +(9.38806 - 16.2606i) q^{97} +(-56.2424 + 78.6338i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.827034	−	1.82099i	−0.413517	−	0.910496i
$2$	−0.827034	−	1.82099i	−0.413517	−	0.910496i
$3$		0			0
$3$		0			0
$4$	−2.63203	+	3.01205i	−0.658007	+	0.753011i
$5$	−3.84571	+	2.22032i	−0.769141	+	0.444064i	−0.832568	−	0.553923i	$-0.813130\pi$
$5$	−3.84571	+	2.22032i	−0.769141	+	0.444064i	0.0634270	+	0.997986i	$0.479797\pi$
$6$		0			0
$7$	0.704321	+	0.406640i	0.100617	+	0.0580915i	0.549464	−	0.835517i	$-0.314832\pi$
$7$	0.704321	+	0.406640i	0.100617	+	0.0580915i	−0.448847	+	0.893609i	$0.648165\pi$
$8$	7.66169	+	2.30184i	0.957711	+	0.287730i
$9$		0			0
$10$	7.22371	+	5.16672i	0.722371	+	0.516672i
$11$	3.72022	−	6.44360i	0.338201	−	0.585782i	−0.645893	−	0.763428i	$-0.723515\pi$
$11$	3.72022	−	6.44360i	0.338201	−	0.585782i	0.984094	+	0.177646i	$0.0568481\pi$
$12$		0			0
$13$	18.0943	−	10.4468i	1.39187	−	0.803598i	0.398349	−	0.917234i	$-0.369583\pi$
$13$	18.0943	−	10.4468i	1.39187	−	0.803598i	0.993522	+	0.113636i	$0.0362498\pi$
$14$	0.157991	−	1.61887i	0.0112851	−	0.115634i
$15$		0			0
$16$	−2.14484	−	15.8556i	−0.134052	−	0.990974i
$17$	−1.74716			−0.102774			−0.0513869	−	0.998679i	$-0.516364\pi$
$17$	−1.74716			−0.102774			−0.0513869	+	0.998679i	$0.516364\pi$
$18$		0			0
$19$	31.7920			1.67326			0.836631	−	0.547767i	$-0.184522\pi$
$19$	31.7920			1.67326			0.836631	+	0.547767i	$0.184522\pi$
$20$	3.43431	−	17.4274i	0.171715	−	0.871369i
$21$		0			0
$22$	−14.8105	−	1.44541i	−0.673205	−	0.0657004i
$23$	6.44927	−	3.72348i	0.280403	−	0.161891i	−0.353203	−	0.935547i	$-0.614907\pi$
$23$	6.44927	−	3.72348i	0.280403	−	0.161891i	0.633606	+	0.773656i	$0.281574\pi$
$24$		0			0
$25$	−2.64036	+	4.57325i	−0.105615	+	0.182930i
$26$	−33.9881	−	24.3098i	−1.30724	−	0.934993i
$27$		0			0
$28$	−3.07861	+	1.05116i	−0.109950	+	0.0375414i
$29$	26.9672	+	15.5695i	0.929904	+	0.536880i	0.886781	−	0.462190i	$-0.152936\pi$
$29$	26.9672	+	15.5695i	0.929904	+	0.536880i	0.0431225	+	0.999070i	$0.486269\pi$
$30$		0			0
$31$	−4.91458	+	2.83744i	−0.158535	+	0.0915302i	−0.577169	−	0.816625i	$-0.695842\pi$
$31$	−4.91458	+	2.83744i	−0.158535	+	0.0915302i	0.418634	+	0.908155i	$0.362509\pi$
$32$	−27.0991	+	17.0188i	−0.846845	+	0.531839i
$33$		0			0
$34$	1.44496	+	3.18156i	0.0424987	+	0.0935753i
$35$	−3.61148			−0.103185
$36$		0			0
$37$		−	62.0787i		−	1.67780i	−0.544283	−	0.838902i	$-0.683198\pi$
$37$		−	62.0787i		−	1.67780i	0.544283	−	0.838902i	$-0.316802\pi$
$38$	−26.2930	−	57.8930i	−0.691922	−	1.52350i
$39$		0			0
$40$	−34.5754	+	8.15919i	−0.864386	+	0.203980i
$41$	−2.74032	−	4.74637i	−0.0668370	−	0.115765i	0.830670	−	0.556765i	$-0.187957\pi$
$41$	−2.74032	−	4.74637i	−0.0668370	−	0.115765i	−0.897507	+	0.440999i	$0.854624\pi$
$42$		0			0
$43$	−22.3782	+	38.7602i	−0.520424	+	0.901401i	0.479294	+	0.877654i	$0.340893\pi$
$43$	−22.3782	+	38.7602i	−0.520424	+	0.901401i	−0.999718	+	0.0237465i	$0.992441\pi$
$44$	9.61671	+	28.1652i	0.218562	+	0.640119i
$45$		0			0
$46$	−12.1142	−	8.66462i	−0.263352	−	0.188361i
$47$	71.1253	+	41.0642i	1.51330	+	0.873707i	0.999879	+	0.0155723i	$0.00495702\pi$
$47$	71.1253	+	41.0642i	1.51330	+	0.873707i	0.513425	+	0.858134i	$0.328376\pi$
$48$		0			0
$49$	−24.1693	−	41.8624i	−0.493251	−	0.854335i
$50$	10.5115	+	1.02586i	0.210230	+	0.0205171i
$51$		0			0
$52$	−16.1587	+	81.9972i	−0.310744	+	1.57687i
$53$		−	85.0348i		−	1.60443i	−0.597035	−	0.802215i	$-0.703655\pi$
$53$		−	85.0348i		−	1.60443i	0.597035	−	0.802215i	$-0.296345\pi$
$54$		0			0
$55$			33.0403i			0.600732i
$56$	4.46027	+	4.73679i	0.0796477	+	0.0845855i
$57$		0			0
$58$	6.04919	−	61.9836i	0.104296	−	1.06868i
$59$	21.8641	+	37.8697i	0.370578	+	0.641860i	0.989655	−	0.143471i	$-0.0458263\pi$
$59$	21.8641	+	37.8697i	0.370578	+	0.641860i	−0.619077	+	0.785331i	$0.712493\pi$
$60$		0			0
$61$	61.1107	+	35.2823i	1.00182	+	0.578398i	0.908785	−	0.417265i	$-0.137011\pi$
$61$	61.1107	+	35.2823i	1.00182	+	0.578398i	0.0930305	+	0.995663i	$0.470345\pi$
$62$	9.23148	+	6.60276i	0.148895	+	0.106496i
$63$		0			0
$64$	53.4030	+	35.2720i	0.834422	+	0.551125i
$65$	−46.3903	+	80.3504i	−0.713697	+	1.23616i
$66$		0			0
$67$	9.91758	+	17.1778i	0.148024	+	0.256384i	0.930497	−	0.366300i	$-0.119376\pi$
$67$	9.91758	+	17.1778i	0.148024	+	0.256384i	−0.782473	+	0.622684i	$0.786042\pi$
$68$	4.59857	−	5.26251i	0.0676260	−	0.0773899i
$69$		0			0
$70$	2.98682	+	6.57649i	0.0426689	+	0.0939498i
$71$			69.3125i			0.976232i	0.872779	+	0.488116i	$0.162316\pi$
$71$			69.3125i			0.976232i	−0.872779	+	0.488116i	$0.837684\pi$
$72$		0			0
$73$	−21.7177			−0.297502			−0.148751	−	0.988875i	$-0.547525\pi$
$73$	−21.7177			−0.297502			−0.148751	+	0.988875i	$0.547525\pi$
$74$	−113.045	+	51.3412i	−1.52763	+	0.693800i
$75$		0			0
$76$	−83.6774	+	95.7589i	−1.10102	+	1.25999i
$77$	5.24046	−	3.02558i	0.0680579	−	0.0392932i
$78$		0			0
$79$	−37.1475	−	21.4471i	−0.470221	−	0.271482i	0.246111	−	0.969242i	$-0.420847\pi$
$79$	−37.1475	−	21.4471i	−0.470221	−	0.271482i	−0.716332	+	0.697759i	$0.754180\pi$
$80$	43.4529	+	56.2137i	0.543161	+	0.702671i
$81$		0			0
$82$	−6.37677	+	8.91551i	−0.0777655	+	0.108726i
$83$	3.53270	−	6.11881i	0.0425626	−	0.0737206i	−0.843959	−	0.536407i	$-0.819781\pi$
$83$	3.53270	−	6.11881i	0.0425626	−	0.0737206i	0.886522	+	0.462687i	$0.153114\pi$
$84$		0			0
$85$	6.71905	−	3.87924i	0.0790476	−	0.0456382i
$86$	89.0897	+	8.69457i	1.03593	+	0.101100i
$87$		0			0
$88$	43.3353	−	40.8055i	0.492447	−	0.463699i
$89$	−37.1192			−0.417070			−0.208535	−	0.978015i	$-0.566870\pi$
$89$	−37.1192			−0.417070			−0.208535	+	0.978015i	$0.566870\pi$
$90$		0			0
$91$	16.9923			0.186729
$92$	−5.75935	+	29.2258i	−0.0626016	+	0.317672i
$93$		0			0
$94$	15.9546	−	163.480i	0.169730	−	1.73915i
$95$	−122.263	+	70.5883i	−1.28697	+	0.743035i
$96$		0			0
$97$	9.38806	−	16.2606i	0.0967841	−	0.167635i	−0.813568	−	0.581470i	$-0.802478\pi$
$97$	9.38806	−	16.2606i	0.0967841	−	0.167635i	0.910352	+	0.413835i	$0.135811\pi$
$98$	−56.2424	+	78.6338i	−0.573902	+	0.802385i
$99$		0			0
$100$	−6.82531	−	19.9898i	−0.0682531	−	0.199898i
$101$	−70.1044	−	40.4748i	−0.694103	−	0.400740i	0.111044	−	0.993815i	$-0.464580\pi$
$101$	−70.1044	−	40.4748i	−0.694103	−	0.400740i	−0.805147	+	0.593075i	$0.797914\pi$
$102$		0			0
$103$	−28.0494	+	16.1943i	−0.272324	+	0.157226i	−0.629943	−	0.776641i	$-0.716922\pi$
$103$	−28.0494	+	16.1943i	−0.272324	+	0.157226i	0.357619	+	0.933867i	$0.383589\pi$
$104$	162.680	−	38.3896i	1.56423	−	0.369131i
$105$		0			0
$106$	−154.848	+	70.3267i	−1.46083	+	0.663459i
$107$	182.822			1.70862			0.854309	−	0.519765i	$-0.173981\pi$
$107$	182.822			1.70862			0.854309	+	0.519765i	$0.173981\pi$
$108$		0			0
$109$		−	7.30063i		−	0.0669782i	−0.999439	−	0.0334891i	$-0.989338\pi$
$109$		−	7.30063i		−	0.0669782i	0.999439	−	0.0334891i	$-0.0106619\pi$
$110$	60.1661	−	27.3254i	0.546964	−	0.248413i
$111$		0			0
$112$	4.93686	−	12.0396i	0.0440791	−	0.107497i
$113$	−70.9810	−	122.943i	−0.628151	−	1.08799i	−0.987923	−	0.154949i	$-0.950479\pi$
$113$	−70.9810	−	122.943i	−0.628151	−	1.08799i	0.359772	−	0.933040i	$-0.382855\pi$
$114$		0			0
$115$	−16.5347	+	28.6389i	−0.143780	+	0.249034i
$116$	−117.875	+	40.2470i	−1.01616	+	0.346957i
$117$		0			0
$118$	50.8781	−	71.1339i	0.431171	−	0.602830i
$119$	−1.23056	−	0.710464i	−0.0103408	−	0.00597028i
$120$		0			0
$121$	32.8200	+	56.8459i	0.271240	+	0.469801i
$122$	13.7082	−	140.462i	0.112362	−	1.15133i
$123$		0			0
$124$	4.38884	−	22.2712i	0.0353939	−	0.179606i
$125$		−	134.466i		−	1.07573i
$126$		0			0
$127$			113.378i			0.892740i	0.894849	+	0.446370i	$0.147283\pi$
$127$			113.378i			0.892740i	−0.894849	+	0.446370i	$0.852717\pi$
$128$	20.0640	−	126.418i	0.156750	−	0.987638i
$129$		0			0
$130$	184.684	+	18.0239i	1.42065	+	0.138646i
$131$	−77.7152	−	134.607i	−0.593245	−	1.02753i	−0.993792	−	0.111255i	$-0.964513\pi$
$131$	−77.7152	−	134.607i	−0.593245	−	1.02753i	0.400546	−	0.916276i	$-0.368820\pi$
$132$		0			0
$133$	22.3918	+	12.9279i	0.168359	+	0.0972022i
$134$	23.0784	−	32.2664i	0.172227	−	0.240794i
$135$		0			0
$136$	−13.3862	−	4.02168i	−0.0984277	−	0.0295712i
$137$	30.9899	−	53.6760i	0.226203	−	0.391796i	−0.730476	−	0.682938i	$-0.760702\pi$
$137$	30.9899	−	53.6760i	0.226203	−	0.391796i	0.956680	+	0.291142i	$0.0940352\pi$
$138$		0			0
$139$	−67.1343	−	116.280i	−0.482981	−	0.836547i	0.516828	−	0.856089i	$-0.327113\pi$
$139$	−67.1343	−	116.280i	−0.482981	−	0.836547i	−0.999809	+	0.0195419i	$0.993779\pi$
$140$	9.50553	−	10.8780i	0.0678967	−	0.0776997i
$141$		0			0
$142$	126.218	−	57.3238i	0.888856	−	0.403689i
$143$		−	155.457i		−	1.08711i
$144$		0			0
$145$	−138.277			−0.953636
$146$	17.9612	+	39.5477i	0.123022	+	0.270875i
$147$		0			0
$148$	186.984	+	163.393i	1.26341	+	1.10401i
$149$	−137.914	+	79.6250i	−0.925600	+	0.534396i	−0.885417	−	0.464797i	$-0.846127\pi$
$149$	−137.914	+	79.6250i	−0.925600	+	0.534396i	−0.0401830	+	0.999192i	$0.512794\pi$
$150$		0			0
$151$	−170.069	−	98.1895i	−1.12629	−	0.650261i	−0.183288	−	0.983059i	$-0.558674\pi$
$151$	−170.069	−	98.1895i	−1.12629	−	0.650261i	−0.942998	+	0.332798i	$0.892007\pi$
$152$	243.580	+	73.1801i	1.60250	+	0.481448i
$153$		0			0
$154$	−9.84359	−	7.04058i	−0.0639194	−	0.0457180i
$155$	12.6000	−	21.8239i	0.0812905	−	0.140799i
$156$		0			0
$157$	−179.848	+	103.835i	−1.14553	+	0.661371i	−0.947794	−	0.318884i	$-0.896692\pi$
$157$	−179.848	+	103.835i	−1.14553	+	0.661371i	−0.197735	+	0.980256i	$0.563358\pi$
$158$	−8.33280	+	85.3827i	−0.0527392	+	0.540397i
$159$		0			0
$160$	66.4277	−	125.618i	0.415173	−	0.785113i
$161$	6.05647			0.0376179
$162$		0			0
$163$	194.579			1.19373			0.596867	−	0.802340i	$-0.296412\pi$
$163$	194.579			1.19373			0.596867	+	0.802340i	$0.296412\pi$
$164$	21.5089	+	4.23862i	0.131152	+	0.0258453i
$165$		0			0
$166$	−14.0640	−	1.37255i	−0.0847228	−	0.00826839i
$167$	−40.2285	+	23.2259i	−0.240889	+	0.139077i	−0.615585	−	0.788070i	$-0.711080\pi$
$167$	−40.2285	+	23.2259i	−0.240889	+	0.139077i	0.374696	+	0.927148i	$0.377747\pi$
$168$		0			0
$169$	133.770	−	231.696i	0.791538	−	1.37098i
$170$	−12.6210	−	9.02707i	−0.0742409	−	0.0531004i
$171$		0			0
$172$	−57.8474	−	169.422i	−0.336322	−	0.985014i
$173$	52.2672	+	30.1765i	0.302123	+	0.174431i	0.643396	−	0.765533i	$-0.277525\pi$
$173$	52.2672	+	30.1765i	0.302123	+	0.174431i	−0.341273	+	0.939964i	$0.610858\pi$
$174$		0			0
$175$	−3.71933	+	2.14736i	−0.0212533	+	0.0122706i
$176$	−110.146	−	45.1657i	−0.625832	−	0.256623i
$177$		0			0
$178$	30.6989	+	67.5938i	0.172465	+	0.379741i
$179$	−123.945			−0.692427			−0.346214	−	0.938156i	$-0.612533\pi$
$179$	−123.945			−0.692427			−0.346214	+	0.938156i	$0.612533\pi$
$180$		0			0
$181$		−	114.095i		−	0.630359i	−0.949032	−	0.315179i	$-0.897935\pi$
$181$		−	114.095i		−	0.630359i	0.949032	−	0.315179i	$-0.102065\pi$
$182$	−14.0532	−	30.9429i	−0.0772154	−	0.170016i
$183$		0			0
$184$	57.9832	−	13.6830i	0.315126	−	0.0743641i
$185$	137.835	+	238.736i	0.745052	+	1.29047i
$186$		0			0
$187$	−6.49980	+	11.2580i	−0.0347583	+	0.0602031i
$188$	−310.891	+	106.150i	−1.65368	+	0.564630i
$189$		0			0
$190$	229.656	+	164.260i	1.20872	+	0.864528i
$191$	12.0842	+	6.97684i	0.0632683	+	0.0365280i	0.531300	−	0.847183i	$-0.321704\pi$
$191$	12.0842	+	6.97684i	0.0632683	+	0.0365280i	−0.468032	+	0.883711i	$0.655037\pi$
$192$		0			0
$193$	30.2654	+	52.4212i	0.156816	+	0.271613i	0.933719	−	0.358008i	$-0.116544\pi$
$193$	30.2654	+	52.4212i	0.156816	+	0.271613i	−0.776903	+	0.629620i	$0.783210\pi$
$194$	−37.3747	−	3.64752i	−0.192653	−	0.0188017i
$195$		0			0
$196$	189.706	+	37.3842i	0.967887	+	0.190736i
$197$			154.506i			0.784296i	0.919902	+	0.392148i	$0.128268\pi$
$197$			154.506i			0.784296i	−0.919902	+	0.392148i	$0.871732\pi$
$198$		0			0
$199$			268.439i			1.34894i	0.738301	+	0.674471i	$0.235628\pi$
$199$			268.439i			1.34894i	−0.738301	+	0.674471i	$0.764372\pi$
$200$	−30.7566	+	28.9611i	−0.153783	+	0.144805i
$201$		0			0
$202$	−15.7256	+	161.134i	−0.0778494	+	0.797691i
$203$	12.6624	+	21.9319i	0.0623763	+	0.108039i
$204$		0			0
$205$	21.0769	+	12.1688i	0.102814	+	0.0593598i
$206$	52.6875	+	37.6845i	0.255765	+	0.182934i
$207$		0			0
$208$	−204.449	−	264.490i	−0.982928	−	1.27158i
$209$	118.273	−	204.855i	0.565900	−	0.980167i
$210$		0			0
$211$	59.5357	+	103.119i	0.282159	+	0.488715i	0.971916	−	0.235326i	$-0.0756159\pi$
$211$	59.5357	+	103.119i	0.282159	+	0.488715i	−0.689757	+	0.724041i	$0.742283\pi$
$212$	256.129	+	223.814i	1.20815	+	1.05573i
$213$		0			0
$214$	−151.200	−	332.918i	−0.706543	−	1.55569i
$215$		−	198.747i		−	0.924406i
$216$		0			0
$217$	−4.61526			−0.0212685
$218$	−13.2944	+	6.03787i	−0.0609834	+	0.0276966i
$219$		0			0
$220$	−99.5188	−	86.9630i	−0.452358	−	0.395286i
$221$	−31.6136	+	18.2521i	−0.143048	+	0.0825888i
$222$		0			0
$223$	93.8558	+	54.1876i	0.420878	+	0.242994i	0.695453	−	0.718572i	$-0.255204\pi$
$223$	93.8558	+	54.1876i	0.420878	+	0.242994i	−0.274575	+	0.961566i	$0.588537\pi$
$224$	−26.0070	+	0.967174i	−0.116103	+	0.00431774i
$225$		0			0
$226$	−165.174	+	230.934i	−0.730859	+	1.02183i
$227$	−135.060	+	233.930i	−0.594977	+	1.03053i	0.398573	+	0.917136i	$0.369505\pi$
$227$	−135.060	+	233.930i	−0.594977	+	1.03053i	−0.993550	+	0.113394i	$0.963828\pi$
$228$		0			0
$229$	−92.7803	+	53.5667i	−0.405154	+	0.233916i	−0.688705	−	0.725041i	$-0.741821\pi$
$229$	−92.7803	+	53.5667i	−0.405154	+	0.233916i	0.283551	+	0.958957i	$0.408487\pi$
$230$	65.8259	+	6.42417i	0.286199	+	0.0279312i
$231$		0			0
$232$	170.776	+	181.363i	0.736103	+	0.781738i
$233$	224.925			0.965344			0.482672	−	0.875801i	$-0.339666\pi$
$233$	224.925			0.965344			0.482672	+	0.875801i	$0.339666\pi$
$234$		0			0
$235$	−364.703			−1.55193
$236$	−171.612	−	33.8186i	−0.727171	−	0.143299i
$237$		0			0
$238$	−0.276035	+	2.82842i	−0.00115981	+	0.0118841i
$239$	77.4022	−	44.6882i	0.323859	−	0.186980i	−0.329253	−	0.944242i	$-0.606797\pi$
$239$	77.4022	−	44.6882i	0.323859	−	0.186980i	0.653111	+	0.757262i	$0.273463\pi$
$240$		0			0
$241$	−135.051	+	233.915i	−0.560377	+	0.970602i	0.437086	+	0.899420i	$0.356010\pi$
$241$	−135.051	+	233.915i	−0.560377	+	0.970602i	−0.997463	+	0.0711821i	$0.977323\pi$
$242$	76.3727	−	106.778i	0.315590	−	0.441233i
$243$		0			0
$244$	−267.117	+	91.2043i	−1.09474	+	0.373788i
$245$	185.896	+	107.327i	0.758759	+	0.438070i
$246$		0			0
$247$	575.255	−	332.123i	2.32897	−	1.34463i
$248$	−44.1853	+	10.4270i	−0.178167	+	0.0420442i
$249$		0			0
$250$	−244.861	+	111.208i	−0.979445	+	0.444831i
$251$	−247.901			−0.987654			−0.493827	−	0.869560i	$-0.664402\pi$
$251$	−247.901			−0.987654			−0.493827	+	0.869560i	$0.664402\pi$
$252$		0			0
$253$		−	55.4087i		−	0.219007i
$254$	206.460	−	93.7674i	0.812836	−	0.369163i
$255$		0			0
$256$	−246.799	+	68.0154i	−0.964060	+	0.265685i
$257$	−43.2996	−	74.9972i	−0.168481	−	0.291818i	0.769405	−	0.638761i	$-0.220553\pi$
$257$	−43.2996	−	74.9972i	−0.168481	−	0.291818i	−0.937886	+	0.346944i	$0.887220\pi$
$258$		0			0
$259$	25.2437	−	43.7234i	0.0974660	−	0.168816i
$260$	−119.918	−	351.214i	−0.461224	−	1.35082i
$261$		0			0
$262$	−180.845	+	252.843i	−0.690247	+	0.965050i
$263$	−36.7606	−	21.2237i	−0.139774	−	0.0806986i	0.428482	−	0.903550i	$-0.359048\pi$
$263$	−36.7606	−	21.2237i	−0.139774	−	0.0806986i	−0.568256	+	0.822852i	$0.692382\pi$
$264$		0			0
$265$	188.804	+	327.019i	0.712470	+	1.23403i
$266$	5.02285	−	51.4671i	0.0188829	−	0.193485i
$267$		0			0
$268$	−77.8435	−	15.3401i	−0.290461	−	0.0572394i
$269$			329.459i			1.22475i	0.790566	+	0.612377i	$0.209786\pi$
$269$			329.459i			1.22475i	−0.790566	+	0.612377i	$0.790214\pi$
$270$		0			0
$271$		−	369.325i		−	1.36282i	−0.731901	−	0.681411i	$-0.761367\pi$
$271$		−	369.325i		−	1.36282i	0.731901	−	0.681411i	$-0.238633\pi$
$272$	3.74737	+	27.7022i	0.0137771	+	0.101846i
$273$		0			0
$274$	−123.373	−	12.0404i	−0.450268	−	0.0439432i
$275$	19.6455	+	34.0269i	0.0714380	+	0.123734i
$276$		0			0
$277$	159.324	+	91.9857i	0.575177	+	0.332078i	0.759214	−	0.650841i	$-0.225583\pi$
$277$	159.324	+	91.9857i	0.575177	+	0.332078i	−0.184038	+	0.982919i	$0.558917\pi$
$278$	−156.223	+	218.419i	−0.561952	+	0.785679i
$279$		0			0
$280$	−27.6701	−	8.31307i	−0.0988217	−	0.0296895i
$281$	−197.079	+	341.350i	−0.701348	+	1.21477i	0.266646	+	0.963795i	$0.414085\pi$
$281$	−197.079	+	341.350i	−0.701348	+	1.21477i	−0.967993	+	0.250976i	$0.919249\pi$
$282$		0			0
$283$	−147.257	−	255.057i	−0.520344	−	0.901262i	−0.999720	−	0.0236524i	$-0.992471\pi$
$283$	−147.257	−	255.057i	−0.520344	−	0.901262i	0.479377	−	0.877609i	$-0.340863\pi$
$284$	−208.772	−	182.433i	−0.735114	−	0.642368i
$285$		0			0
$286$	−283.086	+	128.568i	−0.989811	+	0.449539i
$287$		−	4.45729i		−	0.0155306i
$288$		0			0
$289$	−285.947			−0.989438
$290$	114.360	+	251.802i	0.394345	+	0.868282i
$291$		0			0
$292$	57.1615	−	65.4146i	0.195759	−	0.224023i
$293$	230.417	−	133.031i	0.786406	−	0.454032i	−0.0522899	−	0.998632i	$-0.516652\pi$
$293$	230.417	−	133.031i	0.786406	−	0.454032i	0.838696	+	0.544600i	$0.183319\pi$
$294$		0			0
$295$	−168.166	−	97.0905i	−0.570053	−	0.329120i
$296$	142.895	−	475.628i	0.482755	−	1.60685i
$297$		0			0
$298$	259.056	+	185.289i	0.869317	+	0.621774i
$299$	77.7968	−	134.748i	0.260190	−	0.450662i
$300$		0			0
$301$	−31.5229	+	18.1998i	−0.104727	+	0.0604644i
$302$	−38.1494	+	390.901i	−0.126322	+	1.29437i
$303$		0			0
$304$	−68.1887	−	504.081i	−0.224305	−	1.65816i
$305$	−313.352			−1.02738
$306$		0			0
$307$	104.646			0.340865			0.170433	−	0.985369i	$-0.445483\pi$
$307$	104.646			0.340865			0.170433	+	0.985369i	$0.445483\pi$
$308$	−4.67985	+	23.7479i	−0.0151943	+	0.0771036i
$309$		0			0
$310$	−50.1618	−	4.89546i	−0.161812	−	0.0157918i
$311$	268.616	−	155.085i	0.863716	−	0.498667i	−0.00153895	−	0.999999i	$-0.500490\pi$
$311$	268.616	−	155.085i	0.863716	−	0.498667i	0.865255	+	0.501332i	$0.167157\pi$
$312$		0			0
$313$	201.331	−	348.715i	0.643229	−	1.11411i	−0.341479	−	0.939890i	$-0.610928\pi$
$313$	201.331	−	348.715i	0.643229	−	1.11411i	0.984708	−	0.174216i	$-0.0557390\pi$
$314$	337.824	+	241.627i	1.07587	+	0.769511i
$315$		0			0
$316$	162.373	−	55.4405i	0.513838	−	0.175444i
$317$	162.167	+	93.6269i	0.511566	+	0.295353i	0.733477	−	0.679714i	$-0.237896\pi$
$317$	162.167	+	93.6269i	0.511566	+	0.295353i	−0.221911	+	0.975067i	$0.571229\pi$
$318$		0			0
$319$	200.648	−	115.844i	0.628989	−	0.363147i
$320$	−283.688	−	17.0740i	−0.886523	−	0.0533563i
$321$		0			0
$322$	−5.00891	−	11.0288i	−0.0155556	−	0.0342509i
$323$	−55.5456			−0.171968
$324$		0			0
$325$			110.333i			0.339487i
$326$	−160.923	−	354.326i	−0.493629	−	1.08689i
$327$		0			0
$328$	−10.0701	−	42.6730i	−0.0307015	−	0.130101i
$329$	33.3967	+	57.8448i	0.101510	+	0.175820i
$330$		0			0
$331$	−77.0344	+	133.427i	−0.232732	+	0.403104i	−0.958611	−	0.284718i	$-0.908100\pi$
$331$	−77.0344	+	133.427i	−0.232732	+	0.403104i	0.725879	+	0.687822i	$0.241433\pi$
$332$	9.13198	+	26.7455i	0.0275060	+	0.0805589i
$333$		0			0
$334$	75.5646	+	54.0472i	0.226241	+	0.161818i
$335$	−76.2802	−	44.0404i	−0.227702	−	0.131464i
$336$		0			0
$337$	199.096	+	344.845i	0.590790	+	1.02328i	0.994126	+	0.108226i	$0.0345171\pi$
$337$	199.096	+	344.845i	0.590790	+	1.02328i	−0.403336	+	0.915052i	$0.632150\pi$
$338$	−532.550	−	51.9734i	−1.57559	−	0.153767i
$339$		0			0
$340$	−6.00027	+	30.4484i	−0.0176479	+	0.0895540i
$341$			42.2235i			0.123823i
$342$		0			0
$343$		−	79.1635i		−	0.230798i
$344$	−260.675	+	245.458i	−0.757777	+	0.713540i
$345$		0			0
$346$	11.7244	−	120.135i	0.0338856	−	0.347212i
$347$	211.923	+	367.061i	0.610729	+	1.05781i	0.991118	+	0.132987i	$0.0424569\pi$
$347$	211.923	+	367.061i	0.610729	+	1.05781i	−0.380389	+	0.924827i	$0.624210\pi$
$348$		0			0
$349$	140.567	+	81.1564i	0.402771	+	0.232540i	0.687679	−	0.726015i	$-0.258630\pi$
$349$	140.567	+	81.1564i	0.402771	+	0.232540i	−0.284908	+	0.958555i	$0.591963\pi$
$350$	6.98633	+	4.99694i	0.0199610	+	0.0142770i
$351$		0			0
$352$	8.84836	+	237.929i	0.0251374	+	0.675936i
$353$	162.240	−	281.009i	0.459605	−	0.796059i	−0.539335	−	0.842091i	$-0.681324\pi$
$353$	162.240	−	281.009i	0.459605	−	0.796059i	0.998940	+	0.0460324i	$0.0146577\pi$
$354$		0			0
$355$	−153.896	−	266.555i	−0.433510	−	0.750861i
$356$	97.6989	−	111.805i	0.274435	−	0.314058i
$357$		0			0
$358$	102.506	+	225.702i	0.286331	+	0.630453i
$359$			344.963i			0.960899i	0.877022	+	0.480449i	$0.159526\pi$
$359$			344.963i			0.960899i	−0.877022	+	0.480449i	$0.840474\pi$
$360$		0			0
$361$	649.730			1.79981
$362$	−207.766	+	94.3604i	−0.573939	+	0.260664i
$363$		0			0
$364$	−44.7242	+	51.1816i	−0.122869	+	0.140609i
$365$	83.5197	−	48.2201i	0.228821	−	0.132110i
$366$		0			0
$367$	−16.3628	−	9.44709i	−0.0445854	−	0.0257414i	0.477542	−	0.878609i	$-0.341528\pi$
$367$	−16.3628	−	9.44709i	−0.0445854	−	0.0257414i	−0.522127	+	0.852868i	$0.674861\pi$
$368$	−72.8707	−	94.2706i	−0.198018	−	0.256170i
$369$		0			0
$370$	320.744	−	448.439i	0.866874	−	1.21200i
$371$	34.5786	−	59.8918i	0.0932037	−	0.161434i
$372$		0			0
$373$	−465.036	+	268.489i	−1.24675	+	0.719809i	−0.970459	−	0.241267i	$-0.922437\pi$
$373$	−465.036	+	268.489i	−1.24675	+	0.719809i	−0.276286	+	0.961075i	$0.589104\pi$
$374$	25.8763	+	2.52535i	0.0691878	+	0.00675228i
$375$		0			0
$376$	450.417	+	478.341i	1.19792	+	1.27218i
$377$	650.605			1.72574
$378$		0			0
$379$	439.491			1.15961			0.579804	−	0.814756i	$-0.303129\pi$
$379$	439.491			1.15961			0.579804	+	0.814756i	$0.303129\pi$
$380$	109.183	−	554.051i	0.287325	−	1.45803i
$381$		0			0
$382$	2.71070	−	27.7754i	0.00709607	−	0.0727105i
$383$	225.692	−	130.303i	0.589275	−	0.340218i	−0.175536	−	0.984473i	$-0.556166\pi$
$383$	225.692	−	130.303i	0.589275	−	0.340218i	0.764811	+	0.644255i	$0.222833\pi$
$384$		0			0
$385$	−13.4355	+	23.2710i	−0.0348974	+	0.0604441i
$386$	70.4282	−	98.4672i	0.182456	−	0.255096i
$387$		0			0
$388$	24.2680	+	71.0756i	0.0625464	+	0.183185i
$389$	−166.109	−	95.9029i	−0.427015	−	0.246537i	0.271059	−	0.962563i	$-0.412626\pi$
$389$	−166.109	−	95.9029i	−0.427015	−	0.246537i	−0.698074	+	0.716026i	$0.745959\pi$
$390$		0			0
$391$	−11.2679	+	6.50551i	−0.0288181	+	0.0166381i
$392$	−88.8169	−	376.371i	−0.226574	−	0.960130i
$393$		0			0
$394$	281.355	−	127.782i	0.714098	−	0.324320i
$395$	190.478			0.482222
$396$		0			0
$397$		−	154.843i		−	0.390032i	−0.980800	−	0.195016i	$-0.937524\pi$
$397$		−	154.843i		−	0.390032i	0.980800	−	0.195016i	$-0.0624760\pi$
$398$	488.826	−	222.009i	1.22821	−	0.557810i
$399$		0			0
$400$	78.1747	+	32.0557i	0.195437	+	0.0801391i
$401$	−185.704	−	321.649i	−0.463103	−	0.802118i	0.536010	−	0.844211i	$-0.319931\pi$
$401$	−185.704	−	321.649i	−0.463103	−	0.802118i	−0.999114	+	0.0420930i	$0.986597\pi$
$402$		0			0
$403$	−59.2841	+	102.683i	−0.147107	+	0.254797i
$404$	306.429	−	104.627i	0.758487	−	0.258977i
$405$		0			0
$406$	29.4656	−	41.1965i	0.0725754	−	0.101469i
$407$	−400.011	−	230.946i	−0.982827	−	0.567435i
$408$		0			0
$409$	−95.0595	−	164.648i	−0.232419	−	0.402562i	0.726100	−	0.687589i	$-0.241331\pi$
$409$	−95.0595	−	164.648i	−0.232419	−	0.402562i	−0.958520	+	0.285027i	$0.907997\pi$
$410$	4.72791	−	48.4449i	0.0115315	−	0.118158i
$411$		0			0
$412$	25.0488	−	127.110i	0.0607980	−	0.308519i
$413$			35.5633i			0.0861096i
$414$		0			0
$415$			31.3749i			0.0756021i
$416$	−312.547	+	591.042i	−0.751316	+	1.42077i
$417$		0			0
$418$	−470.855	−	45.9524i	−1.12645	−	0.109934i
$419$	−311.307	−	539.200i	−0.742976	−	1.28687i	−0.951134	−	0.308778i	$-0.900080\pi$
$419$	−311.307	−	539.200i	−0.742976	−	1.28687i	0.208158	−	0.978095i	$-0.433253\pi$
$420$		0			0
$421$	−202.420	−	116.867i	−0.480808	−	0.277595i	0.239945	−	0.970786i	$-0.422871\pi$
$421$	−202.420	−	116.867i	−0.480808	−	0.277595i	−0.720753	+	0.693192i	$0.756204\pi$
$422$	138.541	−	193.697i	0.328295	−	0.458997i
$423$		0			0
$424$	195.737	−	651.510i	0.461643	−	1.53658i
$425$	4.61313	−	7.99018i	0.0108544	−	0.0188004i
$426$		0			0
$427$	28.6944	+	49.7002i	0.0672000	+	0.116394i
$428$	−481.193	+	550.669i	−1.12428	+	1.28661i
$429$		0			0
$430$	−361.917	+	164.371i	−0.841668	+	0.382258i
$431$			458.401i			1.06358i	0.846878	+	0.531788i	$0.178480\pi$
$431$			458.401i			1.06358i	−0.846878	+	0.531788i	$0.821520\pi$
$432$		0			0
$433$	−281.824			−0.650864			−0.325432	−	0.945565i	$-0.605510\pi$
$433$	−281.824			−0.650864			−0.325432	+	0.945565i	$0.605510\pi$
$434$	3.81698	+	8.40436i	0.00879488	+	0.0193649i
$435$		0			0
$436$	21.9898	+	19.2155i	0.0504354	+	0.0440722i
$437$	205.035	−	118.377i	0.469187	−	0.270885i
$438$		0			0
$439$	148.016	+	85.4568i	0.337165	+	0.194662i	0.659018	−	0.752127i	$-0.270972\pi$
$439$	148.016	+	85.4568i	0.337165	+	0.194662i	−0.321853	+	0.946790i	$0.604306\pi$
$440$	−76.0535	+	253.144i	−0.172849	+	0.575328i
$441$		0			0
$442$	59.3825	+	42.4730i	0.134350	+	0.0960929i
$443$	14.6968	−	25.4556i	0.0331756	−	0.0574618i	−0.848961	−	0.528456i	$-0.822771\pi$
$443$	14.6968	−	25.4556i	0.0331756	−	0.0574618i	0.882136	+	0.470994i	$0.156105\pi$
$444$		0			0
$445$	142.750	−	82.4165i	0.320786	−	0.185206i
$446$	21.0534	−	215.726i	0.0472050	−	0.483690i
$447$		0			0
$448$	23.2699	+	46.5587i	0.0519417	+	0.103926i
$449$	−426.134			−0.949074			−0.474537	−	0.880236i	$-0.657384\pi$
$449$	−426.134			−0.949074			−0.474537	+	0.880236i	$0.657384\pi$
$450$		0			0
$451$	−40.7783			−0.0904175
$452$	557.133	+	109.791i	1.23260	+	0.242900i
$453$		0			0
$454$	537.684	+	52.4745i	1.18433	+	0.115583i
$455$	−65.3474	+	37.7283i	−0.143621	+	0.0829194i
$456$		0			0
$457$	−178.504	+	309.178i	−0.390600	+	0.676539i	−0.992529	−	0.122011i	$-0.961066\pi$
$457$	−178.504	+	309.178i	−0.390600	+	0.676539i	0.601929	+	0.798550i	$0.294399\pi$
$458$	174.277	+	124.651i	0.380517	+	0.272163i
$459$		0			0
$460$	−42.7419	−	125.181i	−0.0929171	−	0.272134i
$461$	−724.146	−	418.086i	−1.57082	−	0.906911i	−0.996069	−	0.0885790i	$-0.971767\pi$
$461$	−724.146	−	418.086i	−1.57082	−	0.906911i	−0.574746	−	0.818332i	$-0.694899\pi$
$462$		0			0
$463$	−401.085	+	231.566i	−0.866274	+	0.500143i	−0.866108	−	0.499857i	$-0.833386\pi$
$463$	−401.085	+	231.566i	−0.866274	+	0.500143i	−0.000165490		1.00000i	$0.500053\pi$
$464$	189.024	−	460.975i	0.407378	−	0.993481i
$465$		0			0
$466$	−186.021	−	409.587i	−0.399186	−	0.878942i
$467$	−221.217			−0.473698			−0.236849	−	0.971546i	$-0.576115\pi$
$467$	−221.217			−0.473698			−0.236849	+	0.971546i	$0.576115\pi$
$468$		0			0
$469$			16.1315i			0.0343956i
$470$	301.621	+	664.121i	0.641748	+	1.41302i
$471$		0			0
$472$	80.3458	+	340.474i	0.170224	+	0.721343i
$473$	166.504	+	288.393i	0.352016	+	0.609710i
$474$		0			0
$475$	−83.9424	+	145.393i	−0.176721	+	0.306090i
$476$	5.37882	−	1.83654i	0.0113000	−	0.00385828i
$477$		0			0
$478$	−145.391	−	103.990i	−0.304166	−	0.217553i
$479$	−496.351	−	286.569i	−1.03622	−	0.598264i	−0.117463	−	0.993077i	$-0.537476\pi$
$479$	−496.351	−	286.569i	−1.03622	−	0.598264i	−0.918761	+	0.394813i	$0.870809\pi$
$480$		0			0
$481$	−648.522	−	1123.27i	−1.34828	−	2.33529i
$482$	537.649	+	52.4711i	1.11545	+	0.108861i
$483$		0			0
$484$	−257.606	−	50.7647i	−0.532243	−	0.104886i
$485$			83.3779i			0.171913i
$486$		0			0
$487$			391.908i			0.804739i	0.915477	+	0.402369i	$0.131813\pi$
$487$			391.908i			0.804739i	−0.915477	+	0.402369i	$0.868187\pi$
$488$	386.997	+	410.989i	0.793027	+	0.842191i
$489$		0			0
$490$	41.6996	−	427.278i	0.0851012	−	0.871997i
$491$	58.8904	+	102.001i	0.119940	+	0.207742i	0.919744	−	0.392520i	$-0.128397\pi$
$491$	58.8904	+	102.001i	0.119940	+	0.207742i	−0.799804	+	0.600261i	$0.795063\pi$
$492$		0			0
$493$	−47.1159	−	27.2024i	−0.0955698	−	0.0551773i
$494$	−1080.55	−	772.857i	−2.18735	−	1.56449i
$495$		0			0
$496$	55.5302	+	71.8378i	0.111956	+	0.144834i
$497$	−28.1852	+	48.8183i	−0.0567108	+	0.0982259i
$498$		0			0
$499$	30.7207	+	53.2099i	0.0615646	+	0.106633i	0.895165	−	0.445735i	$-0.147058\pi$
$499$	30.7207	+	53.2099i	0.0615646	+	0.106633i	−0.833600	+	0.552368i	$0.813724\pi$
$500$	405.017	+	353.918i	0.810034	+	0.707836i
$501$		0			0
$502$	205.023	+	451.426i	0.408412	+	0.899256i
$503$		−	284.541i		−	0.565688i	−0.959166	−	0.282844i	$-0.908722\pi$
$503$		−	284.541i		−	0.565688i	0.959166	−	0.282844i	$-0.0912779\pi$
$504$		0			0
$505$	359.468			0.711817
$506$	−100.899	+	45.8249i	−0.199405	+	0.0905630i
$507$		0			0
$508$	−341.500	−	298.414i	−0.672243	−	0.587429i
$509$	−445.430	+	257.169i	−0.875109	+	0.505244i	−0.869043	−	0.494737i	$-0.835264\pi$
$509$	−445.430	+	257.169i	−0.875109	+	0.505244i	−0.00606608	+	0.999982i	$0.501931\pi$
$510$		0			0
$511$	−15.2962	−	8.83127i	−0.0299339	−	0.0172823i
$512$	327.967	+	393.169i	0.640560	+	0.767908i
$513$		0			0
$514$	−100.759	+	140.874i	−0.196029	+	0.274073i
$515$	71.9131	−	124.557i	0.139637	−	0.241859i
$516$		0			0
$517$	529.203	−	305.535i	1.02360	−	0.590978i
$518$	−100.497	−	9.80788i	−0.194010	−	0.0189341i
$519$		0			0
$520$	−540.382	+	508.837i	−1.03920	+	0.978532i
$521$	−208.517			−0.400224			−0.200112	−	0.979773i	$-0.564131\pi$
$521$	−208.517			−0.400224			−0.200112	+	0.979773i	$0.564131\pi$
$522$		0			0
$523$	−17.5861			−0.0336254			−0.0168127	−	0.999859i	$-0.505352\pi$
$523$	−17.5861			−0.0336254			−0.0168127	+	0.999859i	$0.505352\pi$
$524$	609.990	+	120.207i	1.16410	+	0.229403i
$525$		0			0
$526$	−8.24602	+	84.4935i	−0.0156768	+	0.160634i
$527$	8.58654	−	4.95744i	0.0162933	−	0.00940691i
$528$		0			0
$529$	−236.771	+	410.100i	−0.447583	+	0.775236i
$530$	439.351	−	614.267i	0.828965	−	1.15899i
$531$		0			0
$532$	−97.8752	+	33.4184i	−0.183976	+	0.0628166i
$533$	−99.1685	−	57.2549i	−0.186057	−	0.107420i
$534$		0			0
$535$	−703.080	+	405.924i	−1.31417	+	0.758736i
$536$	36.4449	+	154.439i	0.0679943	+	0.288133i
$537$		0			0
$538$	599.942	−	272.474i	1.11513	−	0.506456i
$539$	−359.660			−0.667273
$540$		0			0
$541$		−	476.226i		−	0.880271i	−0.897931	−	0.440135i	$-0.854930\pi$
$541$		−	476.226i		−	0.880271i	0.897931	−	0.440135i	$-0.145070\pi$
$542$	−672.537	+	305.444i	−1.24084	+	0.563550i
$543$		0			0
$544$	47.3463	−	29.7346i	0.0870336	−	0.0546592i
$545$	16.2097	+	28.0761i	0.0297426	+	0.0515157i
$546$		0			0
$547$	−64.5016	+	111.720i	−0.117919	+	0.204241i	−0.918943	−	0.394391i	$-0.870956\pi$
$547$	−64.5016	+	111.720i	−0.117919	+	0.204241i	0.801024	+	0.598632i	$0.204289\pi$
$548$	80.1084	+	234.620i	0.146183	+	0.428138i
$549$		0			0
$550$	45.7153	−	63.9157i	0.0831188	−	0.116210i
$551$	857.341	+	494.986i	1.55597	+	0.898341i
$552$		0			0
$553$	−17.4425	−	30.2113i	−0.0315416	−	0.0546316i
$554$	35.7390	−	366.203i	0.0645109	−	0.661016i
$555$		0			0
$556$	526.940	+	103.841i	0.947735	+	0.186764i
$557$		−	325.840i		−	0.584991i	−0.956267	−	0.292495i	$-0.905514\pi$
$557$		−	325.840i		−	0.584991i	0.956267	−	0.292495i	$-0.0944856\pi$
$558$		0			0
$559$			935.121i			1.67285i
$560$	7.74605	+	57.2622i	0.0138322	+	0.102254i
$561$		0			0
$562$	784.587	+	76.5706i	1.39606	+	0.136247i
$563$	372.114	+	644.521i	0.660949	+	1.14480i	0.980367	+	0.197183i	$0.0631794\pi$
$563$	372.114	+	644.521i	0.660949	+	1.14480i	−0.319418	+	0.947614i	$0.603487\pi$
$564$		0			0
$565$	545.944	+	315.201i	0.966273	+	0.557878i
$566$	−342.670	+	479.095i	−0.605425	+	0.846458i
$567$		0			0
$568$	−159.546	+	531.051i	−0.280892	+	0.934949i
$569$	128.890	−	223.244i	0.226520	−	0.392344i	−0.730255	−	0.683175i	$-0.760599\pi$
$569$	128.890	−	223.244i	0.226520	−	0.392344i	0.956774	+	0.290831i	$0.0939319\pi$
$570$		0			0
$571$	300.850	+	521.087i	0.526883	+	0.912587i	0.999509	+	0.0313247i	$0.00997259\pi$
$571$	300.850	+	521.087i	0.526883	+	0.912587i	−0.472627	+	0.881263i	$0.656694\pi$
$572$	468.243	+	409.167i	0.818607	+	0.715327i
$573$		0			0
$574$	−8.11670	+	3.68633i	−0.0141406	+	0.00642218i
$575$			39.3254i			0.0683921i
$576$		0			0
$577$	−1095.59			−1.89878			−0.949388	−	0.314105i	$-0.898296\pi$
$577$	−1095.59			−1.89878			−0.949388	+	0.314105i	$0.898296\pi$
$578$	236.488	+	520.708i	0.409149	+	0.900879i
$579$		0			0
$580$	363.950	−	416.497i	0.627500	−	0.718099i
$581$	4.97631	−	2.87307i	0.00856508	−	0.00494505i
$582$		0			0
$583$	−547.931	−	316.348i	−0.939847	−	0.542621i
$584$	−166.394	−	49.9906i	−0.284921	−	0.0856004i
$585$		0			0
$586$	−432.812	−	309.566i	−0.738586	−	0.528270i
$587$	229.342	−	397.231i	0.390701	−	0.676714i	−0.601841	−	0.798616i	$-0.705566\pi$
$587$	229.342	−	397.231i	0.390701	−	0.676714i	0.992542	+	0.121902i	$0.0388992\pi$
$588$		0			0
$589$	−156.244	+	90.2077i	−0.265270	+	0.153154i
$590$	−37.7224	+	386.526i	−0.0639363	+	0.655128i
$591$		0			0
$592$	−984.295	+	133.149i	−1.66266	+	0.224914i
$593$	−660.704			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$593$	−660.704			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$594$		0			0
$595$	6.30983			0.0106048
$596$	123.161	−	624.980i	0.206646	−	1.04862i
$597$		0			0
$598$	−309.716	−	30.2262i	−0.517919	−	0.0505455i
$599$	−787.521	+	454.676i	−1.31473	+	0.759058i	−0.982875	−	0.184274i	$-0.941007\pi$
$599$	−787.521	+	454.676i	−1.31473	+	0.759058i	−0.331852	+	0.943332i	$0.607673\pi$
$600$		0			0
$601$	177.135	−	306.806i	0.294733	−	0.510493i	−0.680189	−	0.733036i	$-0.738103\pi$
$601$	177.135	−	306.806i	0.294733	−	0.510493i	0.974923	+	0.222543i	$0.0714358\pi$
$602$	59.2122	+	42.3512i	0.0983592	+	0.0703509i
$603$		0			0
$604$	743.378	−	253.819i	1.23076	−	0.420229i
$605$	−252.432	−	145.742i	−0.417243	−	0.240895i
$606$		0			0
$607$	−452.946	+	261.509i	−0.746205	+	0.430822i	−0.824321	−	0.566123i	$-0.808443\pi$
$607$	−452.946	+	261.509i	−0.746205	+	0.430822i	0.0781160	+	0.996944i	$0.475110\pi$
$608$	−861.533	+	541.063i	−1.41699	+	0.889906i
$609$		0			0
$610$	259.153	+	570.612i	0.424840	+	0.935429i
$611$	1715.95			2.80843
$612$		0			0
$613$			642.493i			1.04811i	0.851684	+	0.524056i	$0.175582\pi$
$613$			642.493i			1.04811i	−0.851684	+	0.524056i	$0.824418\pi$
$614$	−86.5455	−	190.559i	−0.140954	−	0.310357i
$615$		0			0
$616$	47.1152	−	11.1183i	0.0764857	−	0.0180493i
$617$	489.218	+	847.351i	0.792899	+	1.37334i	0.924165	+	0.381994i	$0.124762\pi$
$617$	489.218	+	847.351i	0.792899	+	1.37334i	−0.131266	+	0.991347i	$0.541904\pi$
$618$		0			0
$619$	297.240	−	514.836i	0.480195	−	0.831721i	−0.519547	−	0.854442i	$-0.673899\pi$
$619$	297.240	−	514.836i	0.480195	−	0.831721i	0.999742	+	0.0227203i	$0.00723273\pi$
$620$	32.5709	+	95.3930i	0.0525337	+	0.153860i
$621$		0			0
$622$	−504.564	−	360.886i	−0.811195	−	0.580203i
$623$	−26.1439	−	15.0942i	−0.0419645	−	0.0242282i
$624$		0			0
$625$	232.548	+	402.785i	0.372077	+	0.644455i
$626$	−801.515	−	78.2226i	−1.28037	−	0.124956i
$627$		0			0
$628$	160.609	−	815.008i	0.255746	−	1.29778i
$629$			108.461i			0.172434i
$630$		0			0
$631$		−	259.788i		−	0.411709i	−0.978583	−	0.205854i	$-0.934003\pi$
$631$		−	259.788i		−	0.411709i	0.978583	−	0.205854i	$-0.0659973\pi$
$632$	−235.245	−	249.829i	−0.372222	−	0.395298i
$633$		0			0
$634$	36.3767	−	372.737i	0.0573764	−	0.587913i
$635$	−251.735	−	436.018i	−0.396433	−	0.686643i
$636$		0			0
$637$	−874.654	−	504.982i	−1.37308	−	0.792750i
$638$	−376.893	−	269.571i	−0.590742	−	0.422525i
$639$		0			0
$640$	203.528	+	530.714i	0.318012	+	0.829240i
$641$	−308.536	+	534.401i	−0.481336	+	0.833698i	−0.999771	−	0.0214189i	$-0.993182\pi$
$641$	−308.536	+	534.401i	−0.481336	+	0.833698i	0.518435	+	0.855117i	$0.326515\pi$
$642$		0			0
$643$	−79.5086	−	137.713i	−0.123653	−	0.214172i	0.797553	−	0.603249i	$-0.206127\pi$
$643$	−79.5086	−	137.713i	−0.123653	−	0.214172i	−0.921205	+	0.389077i	$0.872794\pi$
$644$	−15.9408	+	18.2424i	−0.0247528	+	0.0283267i
$645$		0			0
$646$	45.9381	+	101.148i	0.0711115	+	0.156576i
$647$		−	53.2623i		−	0.0823219i	−0.999153	−	0.0411610i	$-0.986894\pi$
$647$		−	53.2623i		−	0.0823219i	0.999153	−	0.0411610i	$-0.0131056\pi$
$648$		0			0
$649$	325.357			0.501320
$650$	200.916	−	91.2492i	0.309101	−	0.140383i
$651$		0			0
$652$	−512.137	+	586.080i	−0.785486	+	0.898895i
$653$	971.623	−	560.967i	1.48794	−	0.859061i	0.488032	−	0.872826i	$-0.337715\pi$
$653$	971.623	−	560.967i	1.48794	−	0.859061i	0.999905	+	0.0137652i	$0.00438174\pi$
$654$		0			0
$655$	597.739	+	345.105i	0.912579	+	0.526878i
$656$	−69.3790	+	53.6296i	−0.105761	+	0.0817524i
$657$		0			0
$658$	77.7148	−	108.655i	0.118108	−	0.165129i
$659$	−225.540	+	390.647i	−0.342246	+	0.592788i	−0.984850	−	0.173411i	$-0.944521\pi$
$659$	−225.540	+	390.647i	−0.342246	+	0.592788i	0.642603	+	0.766199i	$0.277854\pi$
$660$		0			0
$661$	593.593	−	342.711i	0.898023	−	0.518474i	0.0214650	−	0.999770i	$-0.493167\pi$
$661$	593.593	−	342.711i	0.898023	−	0.518474i	0.876558	+	0.481296i	$0.159834\pi$
$662$	306.680	+	29.9300i	0.463264	+	0.0452115i
$663$		0			0
$664$	41.1510	−	38.7487i	0.0619744	−	0.0583565i
$665$	−114.816			−0.172656
$666$		0			0
$667$	231.892			0.347663
$668$	35.9250	−	182.301i	0.0537800	−	0.272906i
$669$		0			0
$670$	−17.1109	+	175.329i	−0.0255387	+	0.261684i
$671$	454.690	−	262.516i	0.677631	−	0.391230i
$672$		0			0
$673$	218.694	−	378.790i	0.324954	−	0.562838i	−0.656549	−	0.754284i	$-0.727984\pi$
$673$	218.694	−	378.790i	0.324954	−	0.562838i	0.981503	+	0.191446i	$0.0613177\pi$
$674$	463.300	−	647.751i	0.687389	−	0.961055i
$675$		0			0
$676$	345.794	+	1012.75i	0.511529	+	1.49816i
$677$	326.939	+	188.758i	0.482923	+	0.278815i	0.721634	−	0.692275i	$-0.243392\pi$
$677$	326.939	+	188.758i	0.482923	+	0.278815i	−0.238711	+	0.971091i	$0.576725\pi$
$678$		0			0
$679$	13.2244	−	7.63512i	0.0194763	−	0.0112447i
$680$	60.4087	−	14.2554i	0.0888363	−	0.0209638i
$681$		0			0
$682$	76.8887	−	34.9203i	0.112740	−	0.0512027i
$683$	−1023.64			−1.49874			−0.749371	−	0.662151i	$-0.769644\pi$
$683$	−1023.64			−1.49874			−0.749371	+	0.662151i	$0.769644\pi$
$684$		0			0
$685$			275.230i			0.401795i
$686$	−144.156	+	65.4709i	−0.210140	+	0.0954387i
$687$		0			0
$688$	662.564	+	271.686i	0.963029	+	0.394892i
$689$	−888.339	−	1538.65i	−1.28932	−	2.23316i
$690$		0			0
$691$	134.426	−	232.833i	0.194539	−	0.336951i	−0.752210	−	0.658923i	$-0.771012\pi$
$691$	134.426	−	232.833i	0.194539	−	0.336951i	0.946749	+	0.321972i	$0.104346\pi$
$692$	−228.462	+	78.0058i	−0.330147	+	0.112725i
$693$		0			0
$694$	493.149	−	689.483i	0.710589	−	0.993491i
$695$	516.358	+	298.119i	0.742961	+	0.428949i
$696$		0			0
$697$	4.78776	+	8.29265i	0.00686910	+	0.0118976i
$698$	31.5315	−	323.091i	0.0451741	−	0.462880i
$699$		0			0
$700$	3.32145	−	16.8547i	0.00474493	−	0.0240781i
$701$		−	888.158i		−	1.26699i	−0.773748	−	0.633494i	$-0.781620\pi$
$701$		−	888.158i		−	1.26699i	0.773748	−	0.633494i	$-0.218380\pi$
$702$		0			0
$703$		−	1973.61i		−	2.80740i
$704$	425.950	−	212.888i	0.605042	−	0.302398i
$705$		0			0
$706$	−645.893	−	63.0350i	−0.914863	−	0.0892847i
$707$	−32.9173	−	57.0145i	−0.0465592	−	0.0806429i
$708$		0			0
$709$	−158.288	−	91.3877i	−0.223256	−	0.128897i	0.384201	−	0.923249i	$-0.374477\pi$
$709$	−158.288	−	91.3877i	−0.223256	−	0.128897i	−0.607457	+	0.794353i	$0.707810\pi$
$710$	−358.119	+	500.694i	−0.504392	+	0.705202i
$711$		0			0
$712$	−284.396	−	85.4426i	−0.399433	−	0.120004i
$713$	−21.1303	+	36.5987i	−0.0296358	+	0.0513306i
$714$		0			0
$715$	345.164	+	597.842i	0.482747	+	0.836142i
$716$	326.226	−	373.327i	0.455622	−	0.521406i
$717$		0			0
$718$	628.175	−	285.296i	0.874895	−	0.397348i
$719$			1086.03i			1.51047i	0.655454	+	0.755235i	$0.272477\pi$
$719$			1086.03i			1.51047i	−0.655454	+	0.755235i	$0.727523\pi$
$720$		0			0
$721$	−26.3410			−0.0365340
$722$	−537.349	−	1183.15i	−0.744250	−	1.63872i
$723$		0			0
$724$	343.659	+	300.301i	0.474667	+	0.414781i
$725$	−142.407	+	82.2184i	−0.196423	+	0.113405i
$726$		0			0
$727$	672.535	+	388.288i	0.925082	+	0.534096i	0.885253	−	0.465110i	$-0.153985\pi$
$727$	672.535	+	388.288i	0.925082	+	0.534096i	0.0398294	+	0.999206i	$0.487319\pi$
$728$	130.190	+	39.1136i	0.178832	+	0.0537275i
$729$		0			0
$730$	−156.882	−	112.209i	−0.214907	−	0.153711i
$731$	39.0983	−	67.7202i	0.0534860	−	0.0926405i
$732$		0			0
$733$	1046.17	−	604.007i	1.42724	−	0.824020i	0.430342	−	0.902666i	$-0.358393\pi$
$733$	1046.17	−	604.007i	1.42724	−	0.824020i	0.996903	+	0.0786463i	$0.0250598\pi$
$734$	−3.67046	+	37.6097i	−0.00500063	+	0.0512394i
$735$		0			0
$736$	−111.400	+	210.662i	−0.151358	+	0.286226i
$737$	147.582			0.200247
$738$		0			0
$739$	−1269.30			−1.71759			−0.858794	−	0.512322i	$-0.828786\pi$
$739$	−1269.30			−1.71759			−0.858794	+	0.512322i	$0.828786\pi$
$740$	−1081.87	−	213.197i	−1.46199	−	0.288105i
$741$		0			0
$742$	−137.660	−	13.4347i	−0.185526	−	0.0181061i
$743$	−49.1224	+	28.3609i	−0.0661136	+	0.0381707i	−0.532692	−	0.846309i	$-0.678820\pi$
$743$	−49.1224	+	28.3609i	−0.0661136	+	0.0381707i	0.466579	+	0.884480i	$0.345486\pi$
$744$		0			0
$745$	353.586	−	612.428i	0.474612	−	0.822051i
$746$	873.516	+	624.778i	1.17093	+	0.837504i
$747$		0			0
$748$	−16.8019	−	49.2090i	−0.0224624	−	0.0657875i
$749$	128.766	+	74.3428i	0.171917	+	0.0992561i
$750$		0			0
$751$	−79.1677	+	45.7075i	−0.105416	+	0.0608622i	−0.551781	−	0.833989i	$-0.686052\pi$
$751$	−79.1677	+	45.7075i	−0.105416	+	0.0608622i	0.446365	+	0.894851i	$0.352718\pi$
$752$	498.545	−	1215.81i	0.662958	−	1.61677i
$753$		0			0
$754$	−538.072	−	1184.75i	−0.713624	−	1.57128i
$755$	872.048			1.15503
$756$		0			0
$757$		−	883.777i		−	1.16747i	−0.811943	−	0.583736i	$-0.801590\pi$
$757$		−	883.777i		−	1.16747i	0.811943	−	0.583736i	$-0.198410\pi$
$758$	−363.474	−	800.310i	−0.479517	−	1.05582i
$759$		0			0
$760$	−1099.22	+	259.397i	−1.44634	+	0.341312i
$761$	210.778	+	365.078i	0.276975	+	0.479734i	0.970631	−	0.240571i	$-0.0773348\pi$
$761$	210.778	+	365.078i	0.276975	+	0.479734i	−0.693657	+	0.720306i	$0.744001\pi$
$762$		0			0
$763$	2.96873	−	5.14199i	0.00389086	−	0.00673917i
$764$	−52.8206	+	18.0350i	−0.0691370	+	0.0236061i
$765$		0			0
$766$	−423.937	−	303.218i	−0.553442	−	0.395847i
$767$	791.232	+	456.818i	1.03159	+	0.595591i
$768$		0			0
$769$	−37.4028	−	64.7836i	−0.0486383	−	0.0842440i	0.840681	−	0.541530i	$-0.182155\pi$
$769$	−37.4028	−	64.7836i	−0.0486383	−	0.0842440i	−0.889320	+	0.457286i	$0.848821\pi$
$770$	53.4879	+	5.22007i	0.0694648	+	0.00677931i
$771$		0			0
$772$	−237.555	−	46.8134i	−0.307713	−	0.0606392i
$773$		−	723.612i		−	0.936108i	−0.883700	−	0.468054i	$-0.844955\pi$
$773$		−	723.612i		−	0.936108i	0.883700	−	0.468054i	$-0.155045\pi$
$774$		0			0
$775$		−	29.9675i		−	0.0386677i
$776$	109.358	−	102.974i	0.140925	−	0.132698i
$777$		0			0
$778$	−37.2610	+	381.798i	−0.0478933	+	0.490742i
$779$	−87.1202	−	150.897i	−0.111836	−	0.193705i
$780$		0			0
$781$	446.622	+	257.857i	0.571859	+	0.330163i
$782$	21.1654	+	15.1384i	0.0270657	+	0.0193586i
$783$		0			0
$784$	−611.914	+	473.006i	−0.780503	+	0.603325i
$785$	461.095	−	798.640i	0.587382	−	1.01738i
$786$		0			0
$787$	608.548	+	1054.04i	0.773251	+	1.33931i	0.935773	+	0.352604i	$0.114704\pi$
$787$	608.548	+	1054.04i	0.773251	+	1.33931i	−0.162522	+	0.986705i	$0.551963\pi$
$788$	−465.380	−	406.665i	−0.590583	−	0.516072i
$789$		0			0
$790$	−157.531	−	346.858i	−0.199407	−	0.439061i
$791$		−	115.455i		−	0.145961i
$792$		0			0
$793$	1474.34			1.85920
$794$	−281.968	+	128.060i	−0.355123	+	0.161285i
$795$		0			0
$796$	−808.552	−	706.541i	−1.01577	−	0.887614i
$797$	−571.321	+	329.853i	−0.716840	+	0.413868i	−0.813588	−	0.581441i	$-0.802489\pi$
$797$	−571.321	+	329.853i	−0.716840	+	0.413868i	0.0967485	+	0.995309i	$0.469156\pi$
$798$		0			0
$799$	−124.267	−	71.7456i	−0.155528	−	0.0897942i
$800$	−6.27998	−	168.867i	−0.00784998	−	0.211083i
$801$		0			0
$802$	−432.137	+	604.181i	−0.538825	+	0.753343i
$803$	−80.7944	+	139.940i	−0.100616	+	0.174271i
$804$		0			0
$805$	−23.2914	+	13.4473i	−0.0289334	+	0.0167047i
$806$	236.015	+	23.0335i	0.292823	+	0.0285776i
$807$		0			0
$808$	−443.952	−	471.475i	−0.549445	−	0.583508i
$809$	409.864			0.506631			0.253315	−	0.967384i	$-0.418479\pi$
$809$	409.864			0.506631			0.253315	+	0.967384i	$0.418479\pi$
$810$		0			0
$811$	283.012			0.348967			0.174483	−	0.984660i	$-0.444174\pi$
$811$	283.012			0.348967			0.174483	+	0.984660i	$0.444174\pi$
$812$	−99.3877	−	19.5857i	−0.122399	−	0.0241203i
$813$		0			0
$814$	−89.7291	+	919.417i	−0.110232	+	1.12950i
$815$	−748.292	+	432.027i	−0.918150	+	0.530094i
$816$		0			0
$817$	−711.448	+	1232.26i	−0.870806	+	1.50828i
$818$	−221.205	+	309.272i	−0.270422	+	0.378083i
$819$		0			0
$820$	−92.1279	+	31.4561i	−0.112351	+	0.0383611i
$821$	−14.8260	−	8.55980i	−0.0180585	−	0.0104261i	0.490944	−	0.871191i	$-0.336652\pi$
$821$	−14.8260	−	8.55980i	−0.0180585	−	0.0104261i	−0.509002	+	0.860765i	$0.669985\pi$
$822$		0			0
$823$	1015.98	−	586.577i	1.23449	−	0.712731i	0.266524	−	0.963828i	$-0.414125\pi$
$823$	1015.98	−	586.577i	1.23449	−	0.712731i	0.967962	+	0.251098i	$0.0807915\pi$
$824$	−252.183	+	59.5106i	−0.306047	+	0.0722216i
$825$		0			0
$826$	64.7605	−	29.4120i	0.0784025	−	0.0356078i
$827$	−219.406			−0.265304			−0.132652	−	0.991163i	$-0.542349\pi$
$827$	−219.406			−0.265304			−0.132652	+	0.991163i	$0.542349\pi$
$828$		0			0
$829$			1596.80i			1.92618i	0.269180	+	0.963090i	$0.413247\pi$
$829$			1596.80i			1.92618i	−0.269180	+	0.963090i	$0.586753\pi$
$830$	57.1334	−	25.9481i	0.0688354	−	0.0312628i
$831$		0			0
$832$	1334.77	+	80.3346i	1.60429	+	0.0965560i
$833$	42.2275	+	73.1402i	0.0506933	+	0.0878034i
$834$		0			0
$835$	103.138	−	178.640i	0.123519	−	0.213940i
$836$	305.734	+	895.428i	0.365711	+	1.07109i
$837$		0			0
$838$	−724.417	+	1012.82i	−0.864460	+	1.20862i
$839$	−774.395	−	447.097i	−0.922997	−	0.532893i	−0.0384071	−	0.999262i	$-0.512228\pi$
$839$	−774.395	−	447.097i	−0.922997	−	0.532893i	−0.884590	+	0.466370i	$0.845562\pi$
$840$		0			0
$841$	64.3200	+	111.406i	0.0764804	+	0.132468i
$842$	−45.4063	+	465.259i	−0.0539267	+	0.552564i
$843$		0			0
$844$	−467.298	−	92.0876i	−0.553671	−	0.109108i
$845$			1188.05i			1.40597i
$846$		0			0
$847$			53.3837i			0.0630268i
$848$	−1348.28	+	182.386i	−1.58995	+	0.215078i
$849$		0			0
$850$	−18.3653	−	1.79233i	−0.0216062	−	0.00210862i
$851$	−231.149	−	400.362i	−0.271621	−	0.470461i
$852$		0			0
$853$	−997.466	−	575.887i	−1.16936	−	0.675132i	−0.215833	−	0.976430i	$-0.569247\pi$
$853$	−997.466	−	575.887i	−1.16936	−	0.675132i	−0.953530	+	0.301298i	$0.902580\pi$
$854$	66.7724	−	93.3560i	0.0781878	−	0.109316i
$855$		0			0
$856$	1400.73	+	420.828i	1.63636	+	0.491621i
$857$	−548.214	+	949.534i	−0.639689	+	1.10797i	0.345812	+	0.938304i	$0.387604\pi$
$857$	−548.214	+	949.534i	−0.639689	+	1.10797i	−0.985501	+	0.169670i	$0.945730\pi$
$858$		0			0
$859$	−3.03512	−	5.25698i	−0.00353332	−	0.00611989i	0.864253	−	0.503057i	$-0.167791\pi$
$859$	−3.03512	−	5.25698i	−0.00353332	−	0.00611989i	−0.867787	+	0.496937i	$0.834458\pi$
$860$	598.636	+	523.109i	0.696088	+	0.608266i
$861$		0			0
$862$	834.745	−	379.113i	0.968381	−	0.439806i
$863$		−	1246.70i		−	1.44461i	−0.691573	−	0.722306i	$-0.743082\pi$
$863$		−	1246.70i		−	1.44461i	0.691573	−	0.722306i	$-0.256918\pi$
$864$		0			0
$865$	−268.006			−0.309833
$866$	233.078	+	513.200i	0.269143	+	0.592609i
$867$		0			0
$868$	12.1475	−	13.9014i	0.0139948	−	0.0160154i
$869$	−276.393	+	159.576i	−0.318059	+	0.183631i
$870$		0			0
$871$	358.904	+	207.213i	0.412060	+	0.237903i
$872$	16.8049	−	55.9352i	0.0192717	−	0.0641458i
$873$		0			0
$874$	−385.134	−	275.465i	−0.440657	−	0.315178i
$875$	54.6792	−	94.7071i	0.0624905	−	0.108237i
$876$		0			0
$877$	73.4991	−	42.4347i	0.0838074	−	0.0483862i	−0.457511	−	0.889204i	$-0.651259\pi$
$877$	73.4991	−	42.4347i	0.0838074	−	0.0483862i	0.541318	+	0.840818i	$0.317926\pi$
$878$	33.2024	−	340.211i	0.0378159	−	0.387484i
$879$		0			0
$880$	523.873	−	70.8661i	0.595310	−	0.0805296i
$881$	377.451			0.428434			0.214217	−	0.976786i	$-0.431280\pi$
$881$	377.451			0.428434			0.214217	+	0.976786i	$0.431280\pi$
$882$		0			0
$883$	−586.966			−0.664741			−0.332370	−	0.943149i	$-0.607848\pi$
$883$	−586.966			−0.664741			−0.332370	+	0.943149i	$0.607848\pi$
$884$	28.2317	−	143.262i	0.0319363	−	0.162061i
$885$		0			0
$886$	−58.5092	−	5.71012i	−0.0660375	−	0.00644483i
$887$	955.774	−	551.816i	1.07754	−	0.622115i	0.147305	−	0.989091i	$-0.452940\pi$
$887$	955.774	−	551.816i	1.07754	−	0.622115i	0.930230	+	0.366976i	$0.119607\pi$
$888$		0			0
$889$	−46.1040	+	79.8545i	−0.0518605	+	0.0898251i
$890$	−268.139	−	191.785i	−0.301279	−	0.215488i
$891$		0			0
$892$	−410.247	+	140.074i	−0.459918	+	0.157034i
$893$	2261.21	+	1305.51i	2.53215	+	1.46194i
$894$		0			0
$895$	476.654	−	275.196i	0.532574	−	0.307482i
$896$	65.5380	−	80.8799i	0.0731451	−	0.0902677i
$897$		0			0
$898$	352.427	+	775.987i	0.392458	+	0.864128i
$899$	−176.710			−0.196563
$900$		0			0
$901$			148.569i			0.164894i
$902$	33.7250	+	74.2570i	0.0373892	+	0.0823248i
$903$		0			0
$904$	−260.840	−	1105.34i	−0.288540	−	1.22272i
$905$	253.327	+	438.776i	0.279920	+	0.484835i
$906$		0			0
$907$	616.897	−	1068.50i	0.680151	−	1.17806i	−0.294783	−	0.955564i	$-0.595247\pi$
$907$	616.897	−	1068.50i	0.680151	−	1.17806i	0.974934	−	0.222493i	$-0.0714193\pi$
$908$	−349.128	−	1022.52i	−0.384502	−	1.12612i
$909$		0			0
$910$	122.748	+	87.7945i	0.134887	+	0.0964775i
$911$	430.671	+	248.648i	0.472746	+	0.272940i	0.717388	−	0.696673i	$-0.245337\pi$
$911$	430.671	+	248.648i	0.472746	+	0.272940i	−0.244643	+	0.969613i	$0.578671\pi$
$912$		0			0
$913$	−26.2848	−	45.5266i	−0.0287895	−	0.0498649i
$914$	710.641	+	69.3539i	0.777506	+	0.0758795i
$915$		0			0
$916$	82.8550	−	420.448i	0.0904531	−	0.459004i
$917$		−	126.408i		−	0.137850i
$918$		0			0
$919$		−	222.255i		−	0.241845i	−0.992662	−	0.120922i	$-0.961415\pi$
$919$		−	222.255i		−	0.241845i	0.992662	−	0.120922i	$-0.0385852\pi$
$920$	−192.606	+	181.362i	−0.209354	+	0.197133i
$921$		0			0
$922$	−162.438	+	1664.44i	−0.176180	+	1.80524i
$923$	724.092	+	1254.16i	0.784498	+	1.35879i
$924$		0			0
$925$	283.901	+	163.910i	0.306920	+	0.177201i
$926$	753.391	+	538.859i	0.813598	+	0.581921i
$927$		0			0
$928$	−995.761	+	37.0314i	−1.07302	+	0.0399045i
$929$	−481.758	+	834.429i	−0.518577	+	0.898201i	0.481190	+	0.876616i	$0.340205\pi$
$929$	−481.758	+	834.429i	−0.518577	+	0.898201i	−0.999767	+	0.0215848i	$0.993129\pi$
$930$		0			0
$931$	−768.390	−	1330.89i	−0.825338	−	1.42953i
$932$	−592.010	+	677.485i	−0.635204	+	0.726915i
$933$		0			0
$934$	182.954	+	402.835i	0.195882	+	0.431301i
$935$		−	57.7265i		−	0.0617396i
$936$		0			0
$937$	7.75413			0.00827549			0.00413774	−	0.999991i	$-0.498683\pi$
$937$	7.75413			0.00827549			0.00413774	+	0.999991i	$0.498683\pi$
$938$	29.3754	−	13.3413i	0.0313171	−	0.0142232i
$939$		0			0
$940$	959.908	−	1098.50i	1.02118	−	1.16862i
$941$	−407.216	+	235.106i	−0.432748	+	0.249847i	−0.700517	−	0.713636i	$-0.747047\pi$
$941$	−407.216	+	235.106i	−0.432748	+	0.249847i	0.267768	+	0.963483i	$0.413714\pi$
$942$		0			0
$943$	−35.3461	−	20.4071i	−0.0374826	−	0.0216406i
$944$	553.552	−	427.893i	0.586390	−	0.453276i
$945$		0			0
$946$	387.457	−	541.713i	0.409574	−	0.572635i
$947$	−881.063	+	1526.05i	−0.930372	+	1.61145i	−0.147687	+	0.989034i	$0.547183\pi$
$947$	−881.063	+	1526.05i	−0.930372	+	1.61145i	−0.782685	+	0.622418i	$0.786150\pi$
$948$		0			0
$949$	−392.967	+	226.879i	−0.414085	+	0.239072i
$950$	334.182	+	32.6140i	0.351771	+	0.0343305i
$951$		0			0
$952$	−7.79279	−	8.27591i	−0.00818571	−	0.00869318i
$953$	1271.02			1.33371			0.666854	−	0.745188i	$-0.267640\pi$
$953$	1271.02			1.33371			0.666854	+	0.745188i	$0.267640\pi$
$954$		0			0
$955$	−61.9632			−0.0648830
$956$	−69.1220	+	350.760i	−0.0723034	+	0.366903i
$957$		0			0
$958$	−111.340	+	1140.85i	−0.116221	+	1.19087i
$959$	43.6537	−	25.2035i	0.0455200	−	0.0262810i
$960$		0			0
$961$	−464.398	+	804.361i	−0.483244	+	0.837004i
$962$	−1509.12	+	2109.94i	−1.56873	+	2.19328i
$963$		0			0
$964$	−349.105	−	1022.45i	−0.362142	−	1.06063i
$965$	−232.784	−	134.398i	−0.241227	−	0.139272i
$966$		0			0
$967$	−1466.93	+	846.934i	−1.51699	+	0.875836i	−0.517192	+	0.855869i	$0.673023\pi$
$967$	−1466.93	+	846.934i	−1.51699	+	0.875836i	−0.999801	+	0.0199668i	$0.993644\pi$
$968$	120.606	+	511.082i	0.124593	+	0.527977i
$969$		0			0
$970$	151.831	−	68.9564i	0.156526	−	0.0710890i
$971$	−1414.92			−1.45717			−0.728587	−	0.684953i	$-0.759823\pi$
$971$	−1414.92			−1.45717			−0.728587	+	0.684953i	$0.759823\pi$
$972$		0			0
$973$		−	109.198i		−	0.112228i
$974$	713.661	−	324.121i	0.732712	−	0.332773i
$975$		0			0
$976$	428.349	−	1044.62i	0.438882	−	1.07031i
$977$	−717.018	−	1241.91i	−0.733897	−	1.27115i	−0.955205	−	0.295944i	$-0.904366\pi$
$977$	−717.018	−	1241.91i	−0.733897	−	1.27115i	0.221308	−	0.975204i	$-0.428967\pi$
$978$		0			0
$979$	−138.092	+	239.182i	−0.141054	+	0.244312i
$980$	−812.558	+	277.439i	−0.829140	+	0.283101i
$981$		0			0
$982$	137.039	−	191.597i	0.139551	−	0.195109i
$983$	−702.617	−	405.656i	−0.714768	−	0.412672i	0.0980558	−	0.995181i	$-0.468738\pi$
$983$	−702.617	−	405.656i	−0.714768	−	0.412672i	−0.812824	+	0.582509i	$0.802071\pi$
$984$		0			0
$985$	−343.053	−	594.185i	−0.348277	−	0.603234i
$986$	−10.5689	+	108.295i	−0.0107190	+	0.109833i
$987$		0			0
$988$	−513.716	+	2606.85i	−0.519956	+	2.63851i
$989$			333.300i			0.337007i
$990$		0			0
$991$			1111.56i			1.12166i	0.827931	+	0.560829i	$0.189518\pi$
$991$			1111.56i			1.12166i	−0.827931	+	0.560829i	$0.810482\pi$
$992$	84.8907	−	160.532i	0.0855753	−	0.161827i
$993$		0			0
$994$	112.208	+	10.9508i	0.112885	+	0.0110169i
$995$	−596.021	−	1032.34i	−0.599016	−	1.03753i
$996$		0			0
$997$	−1017.90	−	587.682i	−1.02096	−	0.589451i	−0.106577	−	0.994304i	$-0.533989\pi$
$997$	−1017.90	−	587.682i	−1.02096	−	0.589451i	−0.914381	+	0.404854i	$0.867322\pi$
$998$	71.4877	−	99.9486i	0.0716310	−	0.100149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.7		40
3.2	odd	2		72.3.p.b.43.14	yes	40
4.3	odd	2		864.3.t.b.559.7		40
8.3	odd	2	inner	216.3.p.b.19.20		40
8.5	even	2		864.3.t.b.559.14		40
9.2	odd	6		648.3.b.f.163.13		20
9.4	even	3	inner	216.3.p.b.91.20		40
9.5	odd	6		72.3.p.b.67.1	yes	40
9.7	even	3		648.3.b.e.163.8		20
12.11	even	2		288.3.t.b.79.12		40
24.5	odd	2		288.3.t.b.79.11		40
24.11	even	2		72.3.p.b.43.1	✓	40
36.7	odd	6		2592.3.b.f.1135.7		20
36.11	even	6		2592.3.b.e.1135.14		20
36.23	even	6		288.3.t.b.175.11		40
36.31	odd	6		864.3.t.b.847.14		40
72.5	odd	6		288.3.t.b.175.12		40
72.11	even	6		648.3.b.f.163.14		20
72.13	even	6		864.3.t.b.847.7		40
72.29	odd	6		2592.3.b.e.1135.7		20
72.43	odd	6		648.3.b.e.163.7		20
72.59	even	6		72.3.p.b.67.14	yes	40
72.61	even	6		2592.3.b.f.1135.14		20
72.67	odd	6	inner	216.3.p.b.91.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.1	✓	40	24.11	even	2
72.3.p.b.43.14	yes	40	3.2	odd	2
72.3.p.b.67.1	yes	40	9.5	odd	6
72.3.p.b.67.14	yes	40	72.59	even	6
216.3.p.b.19.7		40	1.1	even	1	trivial
216.3.p.b.19.20		40	8.3	odd	2	inner
216.3.p.b.91.7		40	72.67	odd	6	inner
216.3.p.b.91.20		40	9.4	even	3	inner
288.3.t.b.79.11		40	24.5	odd	2
288.3.t.b.79.12		40	12.11	even	2
288.3.t.b.175.11		40	36.23	even	6
288.3.t.b.175.12		40	72.5	odd	6
648.3.b.e.163.7		20	72.43	odd	6
648.3.b.e.163.8		20	9.7	even	3
648.3.b.f.163.13		20	9.2	odd	6
648.3.b.f.163.14		20	72.11	even	6
864.3.t.b.559.7		40	4.3	odd	2
864.3.t.b.559.14		40	8.5	even	2
864.3.t.b.847.7		40	72.13	even	6
864.3.t.b.847.14		40	36.31	odd	6
2592.3.b.e.1135.7		20	72.29	odd	6
2592.3.b.e.1135.14		20	36.11	even	6
2592.3.b.f.1135.7		20	36.7	odd	6
2592.3.b.f.1135.14		20	72.61	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.827034 - 1.82099i) q^{2} +(-2.63203 + 3.01205i) q^{4} +(-3.84571 + 2.22032i) q^{5} +(0.704321 + 0.406640i) q^{7} +(7.66169 + 2.30184i) q^{8} +O(q^{10})\)	\(q+(-0.827034 - 1.82099i) q^{2} +(-2.63203 + 3.01205i) q^{4} +(-3.84571 + 2.22032i) q^{5} +(0.704321 + 0.406640i) q^{7} +(7.66169 + 2.30184i) q^{8} +(7.22371 + 5.16672i) q^{10} +(3.72022 - 6.44360i) q^{11} +(18.0943 - 10.4468i) q^{13} +(0.157991 - 1.61887i) q^{14} +(-2.14484 - 15.8556i) q^{16} -1.74716 q^{17} +31.7920 q^{19} +(3.43431 - 17.4274i) q^{20} +(-14.8105 - 1.44541i) q^{22} +(6.44927 - 3.72348i) q^{23} +(-2.64036 + 4.57325i) q^{25} +(-33.9881 - 24.3098i) q^{26} +(-3.07861 + 1.05116i) q^{28} +(26.9672 + 15.5695i) q^{29} +(-4.91458 + 2.83744i) q^{31} +(-27.0991 + 17.0188i) q^{32} +(1.44496 + 3.18156i) q^{34} -3.61148 q^{35} -62.0787i q^{37} +(-26.2930 - 57.8930i) q^{38} +(-34.5754 + 8.15919i) q^{40} +(-2.74032 - 4.74637i) q^{41} +(-22.3782 + 38.7602i) q^{43} +(9.61671 + 28.1652i) q^{44} +(-12.1142 - 8.66462i) q^{46} +(71.1253 + 41.0642i) q^{47} +(-24.1693 - 41.8624i) q^{49} +(10.5115 + 1.02586i) q^{50} +(-16.1587 + 81.9972i) q^{52} -85.0348i q^{53} +33.0403i q^{55} +(4.46027 + 4.73679i) q^{56} +(6.04919 - 61.9836i) q^{58} +(21.8641 + 37.8697i) q^{59} +(61.1107 + 35.2823i) q^{61} +(9.23148 + 6.60276i) q^{62} +(53.4030 + 35.2720i) q^{64} +(-46.3903 + 80.3504i) q^{65} +(9.91758 + 17.1778i) q^{67} +(4.59857 - 5.26251i) q^{68} +(2.98682 + 6.57649i) q^{70} +69.3125i q^{71} -21.7177 q^{73} +(-113.045 + 51.3412i) q^{74} +(-83.6774 + 95.7589i) q^{76} +(5.24046 - 3.02558i) q^{77} +(-37.1475 - 21.4471i) q^{79} +(43.4529 + 56.2137i) q^{80} +(-6.37677 + 8.91551i) q^{82} +(3.53270 - 6.11881i) q^{83} +(6.71905 - 3.87924i) q^{85} +(89.0897 + 8.69457i) q^{86} +(43.3353 - 40.8055i) q^{88} -37.1192 q^{89} +16.9923 q^{91} +(-5.75935 + 29.2258i) q^{92} +(15.9546 - 163.480i) q^{94} +(-122.263 + 70.5883i) q^{95} +(9.38806 - 16.2606i) q^{97} +(-56.2424 + 78.6338i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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