LMFDB - Embedded newform 216.3.p.b.19.20

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			19.20
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99054 - 0.194264i) q^{2} +(3.92452 - 0.773382i) q^{4} +(3.84571 - 2.22032i) q^{5} +(-0.704321 - 0.406640i) q^{7} +(7.66169 - 2.30184i) q^{8} +O(q^{10})$	\(q+(1.99054 - 0.194264i) q^{2} +(3.92452 - 0.773382i) q^{4} +(3.84571 - 2.22032i) q^{5} +(-0.704321 - 0.406640i) q^{7} +(7.66169 - 2.30184i) q^{8} +(7.22371 - 5.16672i) q^{10} +(3.72022 - 6.44360i) q^{11} +(-18.0943 + 10.4468i) q^{13} +(-1.48098 - 0.672610i) q^{14} +(14.8038 - 6.07031i) q^{16} -1.74716 q^{17} +31.7920 q^{19} +(13.3754 - 11.6879i) q^{20} +(6.15349 - 13.5490i) q^{22} +(-6.44927 + 3.72348i) q^{23} +(-2.64036 + 4.57325i) q^{25} +(-33.9881 + 24.3098i) q^{26} +(-3.07861 - 1.05116i) q^{28} +(-26.9672 - 15.5695i) q^{29} +(4.91458 - 2.83744i) q^{31} +(28.2883 - 14.9590i) q^{32} +(-3.47779 + 0.339410i) q^{34} -3.61148 q^{35} +62.0787i q^{37} +(63.2833 - 6.17604i) q^{38} +(24.3538 - 25.8636i) q^{40} +(-2.74032 - 4.74637i) q^{41} +(-22.3782 + 38.7602i) q^{43} +(9.61671 - 28.1652i) q^{44} +(-12.1142 + 8.66462i) q^{46} +(-71.1253 - 41.0642i) q^{47} +(-24.1693 - 41.8624i) q^{49} +(-4.36734 + 9.61617i) q^{50} +(-62.9323 + 54.9924i) q^{52} +85.0348i q^{53} -33.0403i q^{55} +(-6.33232 - 1.49431i) q^{56} +(-56.7040 - 25.7530i) q^{58} +(21.8641 + 37.8697i) q^{59} +(-61.1107 - 35.2823i) q^{61} +(9.23148 - 6.60276i) q^{62} +(53.4030 - 35.2720i) q^{64} +(-46.3903 + 80.3504i) q^{65} +(9.91758 + 17.1778i) q^{67} +(-6.85675 + 1.35122i) q^{68} +(-7.18881 + 0.701581i) q^{70} -69.3125i q^{71} -21.7177 q^{73} +(12.0597 + 123.570i) q^{74} +(124.768 - 24.5873i) q^{76} +(-5.24046 + 3.02558i) q^{77} +(37.1475 + 21.4471i) q^{79} +(43.4529 - 56.2137i) q^{80} +(-6.37677 - 8.91551i) q^{82} +(3.53270 - 6.11881i) q^{83} +(-6.71905 + 3.87924i) q^{85} +(-37.0151 + 81.5012i) q^{86} +(13.6710 - 57.9323i) q^{88} -37.1192 q^{89} +16.9923 q^{91} +(-22.4306 + 19.6006i) q^{92} +(-149.555 - 67.9230i) q^{94} +(122.263 - 70.5883i) q^{95} +(9.38806 - 16.2606i) q^{97} +(-56.2424 - 78.6338i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.99054	−	0.194264i	0.995272	−	0.0971320i
$2$	1.99054	−	0.194264i	0.995272	−	0.0971320i
$3$		0			0
$3$		0			0
$4$	3.92452	−	0.773382i	0.981131	−	0.193345i
$5$	3.84571	−	2.22032i	0.769141	−	0.444064i	−0.0634270	−	0.997986i	$-0.520203\pi$
$5$	3.84571	−	2.22032i	0.769141	−	0.444064i	0.832568	+	0.553923i	$0.186870\pi$
$6$		0			0
$7$	−0.704321	−	0.406640i	−0.100617	−	0.0580915i	0.448847	−	0.893609i	$-0.351835\pi$
$7$	−0.704321	−	0.406640i	−0.100617	−	0.0580915i	−0.549464	+	0.835517i	$0.685168\pi$
$8$	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	−0.993522	−	0.113636i	$-0.963750\pi$
$13$	−18.0943	+	10.4468i	−1.39187	+	0.803598i	−0.398349	+	0.917234i	$0.630417\pi$
$14$	−1.48098	−	0.672610i	−0.105784	−	0.0480436i
$15$		0			0
$16$	14.8038	−	6.07031i	0.925235	−	0.379394i
$17$	−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	$0.184522\pi$
$20$	13.3754	−	11.6879i	0.668770	−	0.584395i
$21$		0			0
$22$	6.15349	−	13.5490i	0.279704	−	0.615862i
$23$	−6.44927	+	3.72348i	−0.280403	+	0.161891i	−0.633606	−	0.773656i	$-0.718426\pi$
$23$	−6.44927	+	3.72348i	−0.280403	+	0.161891i	0.353203	+	0.935547i	$0.385093\pi$
$24$		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	−0.0431225	−	0.999070i	$-0.513731\pi$
$29$	−26.9672	−	15.5695i	−0.929904	−	0.536880i	−0.886781	+	0.462190i	$0.847064\pi$
$30$		0			0
$31$	4.91458	−	2.83744i	0.158535	−	0.0915302i	−0.418634	−	0.908155i	$-0.637491\pi$
$31$	4.91458	−	2.83744i	0.158535	−	0.0915302i	0.577169	+	0.816625i	$0.304158\pi$
$32$	28.2883	−	14.9590i	0.884009	−	0.467470i
$33$		0			0
$34$	−3.47779	+	0.339410i	−0.102288	+	0.00998263i
$35$	−3.61148			−0.103185
$36$		0			0
$37$			62.0787i			1.67780i	0.544283	+	0.838902i	$0.316802\pi$
$37$			62.0787i			1.67780i	−0.544283	+	0.838902i	$0.683198\pi$
$38$	63.2833	−	6.17604i	1.66535	−	0.162527i
$39$		0			0
$40$	24.3538	−	25.8636i	0.608845	−	0.646590i
$41$	−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	$-0.995043\pi$
$47$	−71.1253	−	41.0642i	−1.51330	−	0.873707i	−0.513425	−	0.858134i	$-0.671624\pi$
$48$		0			0
$49$	−24.1693	−	41.8624i	−0.493251	−	0.854335i
$50$	−4.36734	+	9.61617i	−0.0873469	+	0.192323i
$51$		0			0
$52$	−62.9323	+	54.9924i	−1.21024	+	1.05755i
$53$			85.0348i			1.60443i	0.597035	+	0.802215i	$0.296345\pi$
$53$			85.0348i			1.60443i	−0.597035	+	0.802215i	$0.703655\pi$
$54$		0			0
$55$		−	33.0403i		−	0.600732i
$56$	−6.33232	−	1.49431i	−0.113077	−	0.0266842i
$57$		0			0
$58$	−56.7040	−	25.7530i	−0.977655	−	0.444018i
$59$	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	−0.0930305	−	0.995663i	$-0.529655\pi$
$61$	−61.1107	−	35.2823i	−1.00182	−	0.578398i	−0.908785	+	0.417265i	$0.862989\pi$
$62$	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	$0.786042\pi$
$68$	−6.85675	+	1.35122i	−0.100835	+	0.0198709i
$69$		0			0
$70$	−7.18881	+	0.701581i	−0.102697	+	0.0100226i
$71$		−	69.3125i		−	0.976232i	−0.872779	−	0.488116i	$-0.837684\pi$
$71$		−	69.3125i		−	0.976232i	0.872779	−	0.488116i	$-0.162316\pi$
$72$		0			0
$73$	−21.7177			−0.297502			−0.148751	−	0.988875i	$-0.547525\pi$
$73$	−21.7177			−0.297502			−0.148751	+	0.988875i	$0.547525\pi$
$74$	12.0597	+	123.570i	0.162968	+	1.66987i
$75$		0			0
$76$	124.768	−	24.5873i	1.64169	−	0.323518i
$77$	−5.24046	+	3.02558i	−0.0680579	+	0.0392932i
$78$		0			0
$79$	37.1475	+	21.4471i	0.470221	+	0.271482i	0.716332	−	0.697759i	$-0.245820\pi$
$79$	37.1475	+	21.4471i	0.470221	+	0.271482i	−0.246111	+	0.969242i	$0.579153\pi$
$80$	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
$86$	−37.0151	+	81.5012i	−0.430408	+	0.947689i
$87$		0			0
$88$	13.6710	−	57.9323i	0.155352	−	0.658321i
$89$	−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
$92$	−22.4306	+	19.6006i	−0.243811	+	0.213050i
$93$		0			0
$94$	−149.555	−	67.9230i	−1.59101	−	0.722585i
$95$	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	0.805147	−	0.593075i	$-0.202086\pi$
$101$	70.1044	+	40.4748i	0.694103	+	0.400740i	−0.111044	+	0.993815i	$0.535420\pi$
$102$		0			0
$103$	28.0494	−	16.1943i	0.272324	−	0.157226i	−0.357619	−	0.933867i	$-0.616411\pi$
$103$	28.0494	−	16.1943i	0.272324	−	0.157226i	0.629943	+	0.776641i	$0.283078\pi$
$104$	−114.586	+	121.690i	−1.10179	+	1.17010i
$105$		0			0
$106$	16.5192	+	169.265i	0.155842	+	1.59684i
$107$	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	$0.0106619\pi$
$109$			7.30063i			0.0669782i	−0.999439	+	0.0334891i	$0.989338\pi$
$110$	−6.41853	−	65.7681i	−0.0583503	−	0.597892i
$111$		0			0
$112$	−12.8950	−	1.74436i	−0.115134	−	0.0155746i
$113$	−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
$122$	−128.498	−	58.3593i	−1.05326	−	0.478355i
$123$		0			0
$124$	17.0930	−	14.9364i	0.137847	−	0.120455i
$125$			134.466i			1.07573i
$126$		0			0
$127$		−	113.378i		−	0.892740i	−0.894849	−	0.446370i	$-0.852717\pi$
$127$		−	113.378i		−	0.892740i	0.894849	−	0.446370i	$-0.147283\pi$
$128$	99.4490	−	80.5848i	0.776945	−	0.629568i
$129$		0			0
$130$	−76.7327	+	168.953i	−0.590252	+	1.29964i
$131$	−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	$0.993779\pi$
$140$	−14.1734	+	2.79306i	−0.101238	+	0.0199504i
$141$		0			0
$142$	−13.4649	−	137.970i	−0.0948234	−	0.971616i
$143$			155.457i			1.08711i
$144$		0			0
$145$	−138.277			−0.953636
$146$	−43.2299	+	4.21896i	−0.296095	+	0.0288970i
$147$		0			0
$148$	48.0105	+	243.629i	0.324396	+	1.64614i
$149$	137.914	−	79.6250i	0.925600	−	0.534396i	0.0401830	−	0.999192i	$-0.487206\pi$
$149$	137.914	−	79.6250i	0.925600	−	0.534396i	0.885417	+	0.464797i	$0.153873\pi$
$150$		0			0
$151$	170.069	+	98.1895i	1.12629	+	0.650261i	0.942998	−	0.332798i	$-0.107993\pi$
$151$	170.069	+	98.1895i	1.12629	+	0.650261i	0.183288	+	0.983059i	$0.441326\pi$
$152$	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	0.197735	−	0.980256i	$-0.436642\pi$
$157$	179.848	−	103.835i	1.14553	−	0.661371i	0.947794	+	0.318884i	$0.103308\pi$
$158$	78.1100	+	35.4750i	0.494367	+	0.224525i
$159$		0			0
$160$	75.5745	−	120.337i	0.472341	−	0.752107i
$161$	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	$0.296412\pi$
$164$	−14.4252	−	16.5079i	−0.0879585	−	0.100658i
$165$		0			0
$166$	5.84332	−	12.8660i	0.0352007	−	0.0775063i
$167$	40.2285	−	23.2259i	0.240889	−	0.139077i	−0.374696	−	0.927148i	$-0.622253\pi$
$167$	40.2285	−	23.2259i	0.240889	−	0.139077i	0.615585	+	0.788070i	$0.288920\pi$
$168$		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	0.341273	−	0.939964i	$-0.389142\pi$
$173$	−52.2672	−	30.1765i	−0.302123	−	0.174431i	−0.643396	+	0.765533i	$0.722475\pi$
$174$		0			0
$175$	3.71933	−	2.14736i	0.0212533	−	0.0122706i
$176$	15.9585	−	117.972i	0.0906735	−	0.670298i
$177$		0			0
$178$	−73.8874	+	7.21093i	−0.415098	+	0.0405108i
$179$	−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	$0.102065\pi$
$181$			114.095i			0.630359i	−0.949032	+	0.315179i	$0.897935\pi$
$182$	33.8239	−	3.30099i	0.185846	−	0.0181373i
$183$		0			0
$184$	−40.8414	+	43.3734i	−0.221964	+	0.235725i
$185$	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	0.468032	−	0.883711i	$-0.344963\pi$
$191$	−12.0842	−	6.97684i	−0.0632683	−	0.0365280i	−0.531300	+	0.847183i	$0.678296\pi$
$192$		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	$0.783210\pi$
$194$	15.5285	−	34.1912i	0.0800437	−	0.176243i
$195$		0			0
$196$	−127.229	−	145.598i	−0.649125	−	0.742847i
$197$		−	154.506i		−	0.784296i	−0.919902	−	0.392148i	$-0.871732\pi$
$197$		−	154.506i		−	0.784296i	0.919902	−	0.392148i	$-0.128268\pi$
$198$		0			0
$199$		−	268.439i		−	1.34894i	−0.738301	−	0.674471i	$-0.764372\pi$
$199$		−	268.439i		−	1.34894i	0.738301	−	0.674471i	$-0.235628\pi$
$200$	−9.70277	+	41.1165i	−0.0485138	+	0.205583i
$201$		0			0
$202$	147.409	+	66.9480i	0.729745	+	0.331426i
$203$	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	$0.742283\pi$
$212$	65.7644	+	333.721i	0.310209	+	1.57416i
$213$		0			0
$214$	363.915	−	35.5158i	1.70054	−	0.165962i
$215$			198.747i			0.924406i
$216$		0			0
$217$	−4.61526			−0.0212685
$218$	1.41825	+	14.5322i	0.00650573	+	0.0666615i
$219$		0			0
$220$	−25.5527	−	129.667i	−0.116149	−	0.589397i
$221$	31.6136	−	18.2521i	0.143048	−	0.0825888i
$222$		0			0
$223$	−93.8558	−	54.1876i	−0.420878	−	0.242994i	0.274575	−	0.961566i	$-0.411463\pi$
$223$	−93.8558	−	54.1876i	−0.420878	−	0.242994i	−0.695453	+	0.718572i	$0.744796\pi$
$224$	−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	−0.283551	−	0.958957i	$-0.591513\pi$
$229$	92.7803	−	53.5667i	0.405154	−	0.233916i	0.688705	+	0.725041i	$0.258179\pi$
$230$	−27.3494	+	60.2190i	−0.118911	+	0.261822i
$231$		0			0
$232$	−242.453	−	57.2146i	−1.04506	−	0.246615i
$233$	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
$236$	115.094	+	131.711i	0.487686	+	0.558099i
$237$		0			0
$238$	2.58750	+	1.17516i	0.0108718	+	0.00493763i
$239$	−77.4022	+	44.6882i	−0.323859	+	0.186980i	−0.653111	−	0.757262i	$-0.726537\pi$
$239$	−77.4022	+	44.6882i	−0.323859	+	0.186980i	0.329253	+	0.944242i	$0.393203\pi$
$240$		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
$248$	31.1227	−	33.0522i	0.125495	−	0.133275i
$249$		0			0
$250$	26.1219	+	267.660i	0.104487	+	1.07064i
$251$	−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
$254$	−22.0253	−	225.684i	−0.0867136	−	0.888518i
$255$		0			0
$256$	182.303	−	179.727i	0.712120	−	0.702058i
$257$	−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	0.568256	−	0.822852i	$-0.307618\pi$
$263$	36.7606	+	21.2237i	0.139774	+	0.0806986i	−0.428482	+	0.903550i	$0.640952\pi$
$264$		0			0
$265$	188.804	+	327.019i	0.712470	+	1.23403i
$266$	−47.0832	−	21.3836i	−0.177005	−	0.0803895i
$267$		0			0
$268$	52.2067	+	59.7444i	0.194801	+	0.222927i
$269$		−	329.459i		−	1.22475i	−0.790566	−	0.612377i	$-0.790214\pi$
$269$		−	329.459i		−	1.22475i	0.790566	−	0.612377i	$-0.209786\pi$
$270$		0			0
$271$			369.325i			1.36282i	0.731901	+	0.681411i	$0.238633\pi$
$271$			369.325i			1.36282i	−0.731901	+	0.681411i	$0.761367\pi$
$272$	−25.8645	+	10.6058i	−0.0950900	+	0.0389918i
$273$		0			0
$274$	51.2594	−	112.865i	0.187078	−	0.411915i
$275$	19.6455	+	34.0269i	0.0714380	+	0.123734i
$276$		0			0
$277$	−159.324	−	91.9857i	−0.575177	−	0.332078i	0.184038	−	0.982919i	$-0.441083\pi$
$277$	−159.324	−	91.9857i	−0.575177	−	0.332078i	−0.759214	+	0.650841i	$0.774417\pi$
$278$	−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	$-0.340863\pi$
$284$	−53.6050	−	272.019i	−0.188750	−	0.957812i
$285$		0			0
$286$	30.1997	+	309.444i	0.105593	+	1.08197i
$287$			4.45729i			0.0155306i
$288$		0			0
$289$	−285.947			−0.989438
$290$	−275.247	+	26.8623i	−0.949127	+	0.0926286i
$291$		0			0
$292$	−85.2314	+	16.7960i	−0.291889	+	0.0575207i
$293$	−230.417	+	133.031i	−0.786406	+	0.454032i	−0.838696	−	0.544600i	$-0.816681\pi$
$293$	−230.417	+	133.031i	−0.786406	+	0.454032i	0.0522899	+	0.998632i	$0.483348\pi$
$294$		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
$302$	357.605	+	162.412i	1.18412	+	0.537788i
$303$		0			0
$304$	470.641	−	192.987i	1.54816	−	0.634826i
$305$	−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	$0.445483\pi$
$308$	−18.2264	+	15.9268i	−0.0591765	+	0.0517105i
$309$		0			0
$310$	20.8413	−	45.8891i	0.0672300	−	0.148029i
$311$	−268.616	+	155.085i	−0.863716	+	0.498667i	−0.865255	−	0.501332i	$-0.832843\pi$
$311$	−268.616	+	155.085i	−0.863716	+	0.498667i	0.00153895	+	0.999999i	$0.499510\pi$
$312$		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	0.221911	−	0.975067i	$-0.428771\pi$
$317$	−162.167	−	93.6269i	−0.511566	−	0.295353i	−0.733477	+	0.679714i	$0.762104\pi$
$318$		0			0
$319$	−200.648	+	115.844i	−0.628989	+	0.363147i
$320$	127.057	−	254.218i	0.397054	−	0.794430i
$321$		0			0
$322$	12.0557	−	1.17655i	0.0374400	−	0.00365390i
$323$	−55.5456			−0.171968
$324$		0			0
$325$		−	110.333i		−	0.339487i
$326$	387.317	−	37.7996i	1.18809	−	0.115950i
$327$		0			0
$328$	−31.9209	−	30.0574i	−0.0973197	−	0.0916386i
$329$	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	$0.632150\pi$
$338$	221.265	−	487.188i	0.654629	−	1.44139i
$339$		0			0
$340$	−23.3689	+	20.4206i	−0.0687321	+	0.0600605i
$341$		−	42.2235i		−	0.123823i
$342$		0			0
$343$			79.1635i			0.230798i
$344$	−82.2352	+	348.480i	−0.239056	+	1.01302i
$345$		0			0
$346$	−109.902	−	49.9140i	−0.317637	−	0.144260i
$347$	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	0.284908	−	0.958555i	$-0.408037\pi$
$349$	−140.567	−	81.1564i	−0.402771	−	0.232540i	−0.687679	+	0.726015i	$0.741370\pi$
$350$	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
$356$	−145.675	+	28.7073i	−0.409200	+	0.0806386i
$357$		0			0
$358$	−246.717	+	24.0780i	−0.689153	+	0.0672569i
$359$		−	344.963i		−	0.960899i	−0.877022	−	0.480449i	$-0.840474\pi$
$359$		−	344.963i		−	0.960899i	0.877022	−	0.480449i	$-0.159526\pi$
$360$		0			0
$361$	649.730			1.79981
$362$	22.1645	+	227.111i	0.0612280	+	0.627378i
$363$		0			0
$364$	66.6867	−	13.1415i	0.183205	−	0.0361031i
$365$	−83.5197	+	48.2201i	−0.228821	+	0.132110i
$366$		0			0
$367$	16.3628	+	9.44709i	0.0445854	+	0.0257414i	0.522127	−	0.852868i	$-0.325139\pi$
$367$	16.3628	+	9.44709i	0.0445854	+	0.0257414i	−0.477542	+	0.878609i	$0.658472\pi$
$368$	−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	0.276286	−	0.961075i	$-0.410896\pi$
$373$	465.036	−	268.489i	1.24675	−	0.719809i	0.970459	+	0.241267i	$0.0775628\pi$
$374$	−10.7511	+	23.6722i	−0.0287463	+	0.0632946i
$375$		0			0
$376$	−639.463	−	150.902i	−1.70070	−	0.401335i
$377$	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	$0.303129\pi$
$380$	425.231	−	371.581i	1.11903	−	0.977845i
$381$		0			0
$382$	−25.4096	−	11.5402i	−0.0665172	−	0.0302099i
$383$	−225.692	+	130.303i	−0.589275	+	0.340218i	−0.764811	−	0.644255i	$-0.777167\pi$
$383$	−225.692	+	130.303i	−0.589275	+	0.340218i	0.175536	+	0.984473i	$0.443834\pi$
$384$		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	0.698074	−	0.716026i	$-0.254041\pi$
$389$	166.109	+	95.9029i	0.427015	+	0.246537i	−0.271059	+	0.962563i	$0.587374\pi$
$390$		0			0
$391$	11.2679	−	6.50551i	0.0288181	−	0.0166381i
$392$	−281.538	−	265.103i	−0.718210	−	0.676284i
$393$		0			0
$394$	−30.0150	−	307.551i	−0.0761802	−	0.780587i
$395$	190.478			0.482222
$396$		0			0
$397$			154.843i			0.390032i	0.980800	+	0.195016i	$0.0624760\pi$
$397$			154.843i			0.390032i	−0.980800	+	0.195016i	$0.937524\pi$
$398$	−52.1481	−	534.340i	−0.131025	−	1.34256i
$399$		0			0
$400$	−11.3263	+	83.7291i	−0.0283158	+	0.209323i
$401$	−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	$0.907997\pi$
$410$	−44.3185	−	20.1280i	−0.108094	−	0.0490926i
$411$		0			0
$412$	97.5561	−	85.2479i	0.236787	−	0.206912i
$413$		−	35.5633i		−	0.0861096i
$414$		0			0
$415$		−	31.3749i		−	0.0756021i
$416$	−355.584	+	566.195i	−0.854769	+	1.36105i
$417$		0			0
$418$	195.632	−	430.749i	0.468018	−	1.03050i
$419$	−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	0.720753	−	0.693192i	$-0.243796\pi$
$421$	202.420	+	116.867i	0.480808	+	0.277595i	−0.239945	+	0.970786i	$0.577129\pi$
$422$	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
$428$	717.490	−	141.391i	1.67638	−	0.330354i
$429$		0			0
$430$	38.6094	+	395.615i	0.0897894	+	0.920035i
$431$		−	458.401i		−	1.06358i	−0.846878	−	0.531788i	$-0.821520\pi$
$431$		−	458.401i		−	1.06358i	0.846878	−	0.531788i	$-0.178480\pi$
$432$		0			0
$433$	−281.824			−0.650864			−0.325432	−	0.945565i	$-0.605510\pi$
$433$	−281.824			−0.650864			−0.325432	+	0.945565i	$0.605510\pi$
$434$	−9.18688	+	0.896579i	−0.0211679	+	0.00206585i
$435$		0			0
$436$	5.64617	+	28.6515i	0.0129499	+	0.0657144i
$437$	−205.035	+	118.377i	−0.469187	+	0.270885i
$438$		0			0
$439$	−148.016	−	85.4568i	−0.337165	−	0.194662i	0.321853	−	0.946790i	$-0.395694\pi$
$439$	−148.016	−	85.4568i	−0.337165	−	0.194662i	−0.659018	+	0.752127i	$0.729028\pi$
$440$	−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
$446$	−197.351	−	89.6300i	−0.442490	−	0.200964i
$447$		0			0
$448$	−51.9559	+	3.12702i	−0.115973	+	0.00697996i
$449$	−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
$452$	−373.648	−	427.596i	−0.826656	−	0.946009i
$453$		0			0
$454$	−223.398	+	491.886i	−0.492066	+	1.08345i
$455$	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	$0.0282326\pi$
$461$	724.146	+	418.086i	1.57082	+	0.906911i	0.574746	+	0.818332i	$0.305101\pi$
$462$		0			0
$463$	401.085	−	231.566i	0.866274	−	0.500143i	0.000165490	−	1.00000i	$-0.499947\pi$
$463$	401.085	−	231.566i	0.866274	−	0.500143i	0.866108	+	0.499857i	$0.166614\pi$
$464$	−493.728	−	66.7883i	−1.06407	−	0.143940i
$465$		0			0
$466$	447.723	−	43.6949i	0.960779	−	0.0937658i
$467$	−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
$470$	−725.956	+	70.8486i	−1.54459	+	0.150742i
$471$		0			0
$472$	254.686	+	239.818i	0.539589	+	0.508090i
$473$	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	0.918761	−	0.394813i	$-0.129191\pi$
$479$	496.351	+	286.569i	1.03622	+	0.598264i	0.117463	+	0.993077i	$0.462524\pi$
$480$		0			0
$481$	−648.522	−	1123.27i	−1.34828	−	2.33529i
$482$	−223.383	+	491.853i	−0.463451	+	1.02044i
$483$		0			0
$484$	172.766	+	197.711i	0.356955	+	0.408493i
$485$		−	83.3779i		−	0.171913i
$486$		0			0
$487$		−	391.908i		−	0.804739i	−0.915477	−	0.402369i	$-0.868187\pi$
$487$		−	391.908i		−	0.804739i	0.915477	−	0.402369i	$-0.131813\pi$
$488$	−549.426	−	129.655i	−1.12587	−	0.265686i
$489$		0			0
$490$	−390.884	−	177.526i	−0.797722	−	0.362298i
$491$	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	$0.813724\pi$
$500$	103.993	+	527.714i	0.207987	+	1.05543i
$501$		0			0
$502$	−493.458	+	48.1583i	−0.982984	+	0.0959328i
$503$			284.541i			0.565688i	0.959166	+	0.282844i	$0.0912779\pi$
$503$			284.541i			0.565688i	−0.959166	+	0.282844i	$0.908722\pi$
$504$		0			0
$505$	359.468			0.711817
$506$	10.7639	+	110.293i	0.0212725	+	0.217971i
$507$		0			0
$508$	−87.6844	−	444.954i	−0.172607	−	0.875894i
$509$	445.430	−	257.169i	0.875109	−	0.505244i	0.00606608	−	0.999982i	$-0.498069\pi$
$509$	445.430	−	257.169i	0.875109	−	0.505244i	0.869043	+	0.494737i	$0.164736\pi$
$510$		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
$518$	41.7548	−	91.9372i	0.0806077	−	0.177485i
$519$		0			0
$520$	−170.474	+	722.403i	−0.327835	+	1.38924i
$521$	−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	$0.505352\pi$
$524$	−409.097	−	468.163i	−0.780720	−	0.893441i
$525$		0			0
$526$	77.2965	+	35.1055i	0.146952	+	0.0667405i
$527$	−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
$536$	115.526	+	108.782i	0.215533	+	0.202951i
$537$		0			0
$538$	−64.0020	−	655.802i	−0.118963	−	1.21896i
$539$	−359.660			−0.667273
$540$		0			0
$541$			476.226i			0.880271i	0.897931	+	0.440135i	$0.145070\pi$
$541$			476.226i			0.880271i	−0.897931	+	0.440135i	$0.854930\pi$
$542$	71.7465	+	735.156i	0.132374	+	1.35638i
$543$		0			0
$544$	−49.4240	+	26.1358i	−0.0908530	+	0.0480437i
$545$	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
$554$	−335.011	−	152.151i	−0.604712	−	0.274640i
$555$		0			0
$556$	−353.399	−	404.423i	−0.635610	−	0.727380i
$557$			325.840i			0.584991i	0.956267	+	0.292495i	$0.0944856\pi$
$557$			325.840i			0.584991i	−0.956267	+	0.292495i	$0.905514\pi$
$558$		0			0
$559$		−	935.121i		−	1.67285i
$560$	−53.4635	+	21.9228i	−0.0954706	+	0.0391479i
$561$		0			0
$562$	−325.982	+	717.758i	−0.580039	+	1.27715i
$563$	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	$0.656694\pi$
$572$	120.228	+	610.094i	0.210188	+	1.06660i
$573$		0			0
$574$	0.865892	+	8.87244i	0.00150852	+	0.0154572i
$575$		−	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	$0.898296\pi$
$578$	−569.191	+	55.5493i	−0.984759	+	0.0961060i
$579$		0			0
$580$	−542.672	+	106.941i	−0.935642	+	0.184381i
$581$	−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
$590$	353.602	+	160.594i	0.599326	+	0.272194i
$591$		0			0
$592$	376.837	+	918.999i	0.636549	+	1.55236i
$593$	−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
$596$	479.668	−	419.150i	0.804812	−	0.703273i
$597$		0			0
$598$	128.681	−	283.335i	0.215186	−	0.473804i
$599$	787.521	−	454.676i	1.31473	−	0.759058i	0.331852	−	0.943332i	$-0.392327\pi$
$599$	787.521	−	454.676i	1.31473	−	0.759058i	0.982875	+	0.184274i	$0.0589933\pi$
$600$		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	−0.0781160	−	0.996944i	$-0.524890\pi$
$607$	452.946	−	261.509i	0.746205	−	0.430822i	0.824321	+	0.566123i	$0.191557\pi$
$608$	899.341	−	475.578i	1.47918	−	0.782200i
$609$		0			0
$610$	−623.740	+	60.8730i	−1.02253	+	0.0997918i
$611$	1715.95			2.80843
$612$		0			0
$613$		−	642.493i		−	1.04811i	−0.851684	−	0.524056i	$-0.824418\pi$
$613$		−	642.493i		−	1.04811i	0.851684	−	0.524056i	$-0.175582\pi$
$614$	208.302	−	20.3289i	0.339254	−	0.0331089i
$615$		0			0
$616$	−33.1863	+	35.2438i	−0.0538739	+	0.0572139i
$617$	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
$626$	333.015	−	733.243i	0.531972	−	1.17132i
$627$		0			0
$628$	625.513	−	546.595i	0.996040	−	0.870374i
$629$		−	108.461i		−	0.172434i
$630$		0			0
$631$			259.788i			0.411709i	0.978583	+	0.205854i	$0.0659973\pi$
$631$			259.788i			0.411709i	−0.978583	+	0.205854i	$0.934003\pi$
$632$	333.980	+	78.8134i	0.528450	+	0.124705i
$633$		0			0
$634$	−340.988	−	154.865i	−0.537836	−	0.244267i
$635$	−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	$0.872794\pi$
$644$	23.7688	−	4.68397i	0.0369080	−	0.00727324i
$645$		0			0
$646$	−110.566	+	10.7905i	−0.171155	+	0.0167036i
$647$			53.2623i			0.0823219i	0.999153	+	0.0411610i	$0.0131056\pi$
$647$			53.2623i			0.0823219i	−0.999153	+	0.0411610i	$0.986894\pi$
$648$		0			0
$649$	325.357			0.501320
$650$	−21.4338	−	219.623i	−0.0329750	−	0.337881i
$651$		0			0
$652$	763.628	−	150.484i	1.17121	−	0.230803i
$653$	−971.623	+	560.967i	−1.48794	+	0.859061i	−0.999905	−	0.0137652i	$-0.995618\pi$
$653$	−971.623	+	560.967i	−1.48794	+	0.859061i	−0.488032	+	0.872826i	$0.662285\pi$
$654$		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	−0.876558	−	0.481296i	$-0.840166\pi$
$661$	−593.593	+	342.711i	−0.898023	+	0.518474i	−0.0214650	+	0.999770i	$0.506833\pi$
$662$	−127.420	+	280.558i	−0.192477	+	0.423804i
$663$		0			0
$664$	12.9819	−	55.0122i	0.0195511	−	0.0828497i
$665$	−114.816			−0.172656
$666$		0			0
$667$	231.892			0.347663
$668$	139.915	−	122.263i	0.209454	−	0.183028i
$669$		0			0
$670$	160.394	+	72.8458i	0.239395	+	0.108725i
$671$	−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	0.238711	−	0.971091i	$-0.423275\pi$
$677$	−326.939	−	188.758i	−0.482923	−	0.278815i	−0.721634	+	0.692275i	$0.756608\pi$
$678$		0			0
$679$	−13.2244	+	7.63512i	−0.0194763	+	0.0112447i
$680$	−42.5499	+	45.1878i	−0.0625733	+	0.0664526i
$681$		0			0
$682$	−8.20250	−	84.0477i	−0.0120271	−	0.123237i
$683$	−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
$686$	15.3786	+	157.578i	0.0224178	+	0.229706i
$687$		0			0
$688$	−95.9955	+	709.640i	−0.139528	+	1.03145i
$689$	−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
$698$	−295.570	−	134.238i	−0.423453	−	0.192318i
$699$		0			0
$700$	12.9359	−	11.3038i	0.0184798	−	0.0161483i
$701$			888.158i			1.26699i	0.773748	+	0.633494i	$0.218380\pi$
$701$			888.158i			1.26699i	−0.773748	+	0.633494i	$0.781620\pi$
$702$		0			0
$703$			1973.61i			2.80740i
$704$	−28.6081	−	475.328i	−0.0406365	−	0.675181i
$705$		0			0
$706$	268.357	−	590.878i	0.380109	−	0.836937i
$707$	−32.9173	−	57.0145i	−0.0465592	−	0.0806429i
$708$		0			0
$709$	158.288	+	91.3877i	0.223256	+	0.128897i	0.607457	−	0.794353i	$-0.292190\pi$
$709$	158.288	+	91.3877i	0.223256	+	0.128897i	−0.384201	+	0.923249i	$0.625523\pi$
$710$	−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
$716$	−486.423	+	95.8564i	−0.679362	+	0.133878i
$717$		0			0
$718$	−67.0138	−	686.663i	−0.0933340	−	0.956355i
$719$		−	1086.03i		−	1.51047i	−0.655454	−	0.755235i	$-0.727523\pi$
$719$		−	1086.03i		−	1.51047i	0.655454	−	0.755235i	$-0.272477\pi$
$720$		0			0
$721$	−26.3410			−0.0365340
$722$	1293.32	−	126.219i	1.79130	−	0.174819i
$723$		0			0
$724$	88.2389	+	447.768i	0.121877	+	0.618464i
$725$	142.407	−	82.2184i	0.196423	−	0.113405i
$726$		0			0
$727$	−672.535	−	388.288i	−0.925082	−	0.534096i	−0.0398294	−	0.999206i	$-0.512681\pi$
$727$	−672.535	−	388.288i	−0.925082	−	0.534096i	−0.885253	+	0.465110i	$0.846015\pi$
$728$	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	−0.996903	−	0.0786463i	$-0.974940\pi$
$733$	−1046.17	+	604.007i	−1.42724	+	0.824020i	−0.430342	+	0.902666i	$0.641607\pi$
$734$	34.4062	+	15.6261i	0.0468749	+	0.0212890i
$735$		0			0
$736$	−126.739	+	201.806i	−0.172200	+	0.274193i
$737$	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	$0.828786\pi$
$740$	725.569	+	830.328i	0.980499	+	1.12207i
$741$		0			0
$742$	57.1953	−	125.935i	0.0770826	−	0.169723i
$743$	49.1224	−	28.3609i	0.0661136	−	0.0381707i	−0.466579	−	0.884480i	$-0.654514\pi$
$743$	49.1224	−	28.3609i	0.0661136	−	0.0381707i	0.532692	+	0.846309i	$0.321180\pi$
$744$		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	−0.446365	−	0.894851i	$-0.647282\pi$
$751$	79.1677	−	45.7075i	0.105416	−	0.0608622i	0.551781	+	0.833989i	$0.313948\pi$
$752$	−1302.19	−	176.152i	−1.73164	−	0.234245i
$753$		0			0
$754$	1295.06	−	126.389i	1.71758	−	0.167625i
$755$	872.048			1.15503
$756$		0			0
$757$			883.777i			1.16747i	0.811943	+	0.583736i	$0.198410\pi$
$757$			883.777i			1.16747i	−0.811943	+	0.583736i	$0.801590\pi$
$758$	874.826	−	85.3773i	1.15412	−	0.112635i
$759$		0			0
$760$	774.255	−	822.255i	1.01876	−	1.08192i
$761$	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	$0.848821\pi$
$770$	−22.2232	+	48.9319i	−0.0288613	+	0.0635479i
$771$		0			0
$772$	159.319	+	182.322i	0.206372	+	0.236168i
$773$			723.612i			0.936108i	0.883700	+	0.468054i	$0.155045\pi$
$773$			723.612i			0.936108i	−0.883700	+	0.468054i	$0.844955\pi$
$774$		0			0
$775$			29.9675i			0.0386677i
$776$	34.4991	−	146.193i	0.0444576	−	0.188394i
$777$		0			0
$778$	349.277	+	158.630i	0.448942	+	0.203894i
$779$	−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	$0.551963\pi$
$788$	−119.492	−	606.363i	−0.151640	−	0.769496i
$789$		0			0
$790$	379.154	−	37.0029i	0.479942	−	0.0468392i
$791$			115.455i			0.145961i
$792$		0			0
$793$	1474.34			1.85920
$794$	30.0804	+	308.221i	0.0378846	+	0.388188i
$795$		0			0
$796$	−207.606	−	1053.50i	−0.260812	−	1.32349i
$797$	571.321	−	329.853i	0.716840	−	0.413868i	−0.0967485	−	0.995309i	$-0.530844\pi$
$797$	571.321	−	329.853i	0.716840	−	0.413868i	0.813588	+	0.581441i	$0.197511\pi$
$798$		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
$806$	−98.0599	+	215.912i	−0.121662	+	0.267881i
$807$		0			0
$808$	630.285	+	148.736i	0.780055	+	0.184079i
$809$	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	$0.444174\pi$
$812$	66.6556	+	76.2794i	0.0820881	+	0.0939401i
$813$		0			0
$814$	841.103	+	382.001i	1.03330	+	0.469288i
$815$	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	0.509002	−	0.860765i	$-0.330015\pi$
$821$	14.8260	+	8.55980i	0.0180585	+	0.0104261i	−0.490944	+	0.871191i	$0.663348\pi$
$822$		0			0
$823$	−1015.98	+	586.577i	−1.23449	+	0.712731i	−0.967962	−	0.251098i	$-0.919208\pi$
$823$	−1015.98	+	586.577i	−1.23449	+	0.712731i	−0.266524	+	0.963828i	$0.585875\pi$
$824$	177.629	−	188.641i	0.215569	−	0.228933i
$825$		0			0
$826$	−6.90866	−	70.7902i	−0.00836400	−	0.0857025i
$827$	−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	$-0.586753\pi$
$829$		−	1596.80i		−	1.92618i	0.269180	−	0.963090i	$-0.413247\pi$
$830$	−6.09501	−	62.4530i	−0.00734338	−	0.0752446i
$831$		0			0
$832$	−597.814	+	1196.11i	−0.718526	+	1.43764i
$833$	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	0.884590	−	0.466370i	$-0.154438\pi$
$839$	774.395	+	447.097i	0.922997	+	0.532893i	0.0384071	+	0.999262i	$0.487772\pi$
$840$		0			0
$841$	64.3200	+	111.406i	0.0764804	+	0.132468i
$842$	425.629	+	193.307i	0.505498	+	0.229580i
$843$		0			0
$844$	313.399	+	358.648i	0.371326	+	0.424939i
$845$		−	1188.05i		−	1.40597i
$846$		0			0
$847$		−	53.3837i		−	0.0630268i
$848$	516.187	+	1258.84i	0.608712	+	1.48448i
$849$		0			0
$850$	7.63043	−	16.8010i	0.00897698	−	0.0197658i
$851$	−231.149	−	400.362i	−0.271621	−	0.470461i
$852$		0			0
$853$	997.466	+	575.887i	1.16936	+	0.675132i	0.953530	−	0.301298i	$-0.0974201\pi$
$853$	997.466	+	575.887i	1.16936	+	0.675132i	0.215833	+	0.976430i	$0.430753\pi$
$854$	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	$0.834458\pi$
$860$	153.708	+	779.988i	0.178730	+	0.906963i
$861$		0			0
$862$	−89.0508	−	912.467i	−0.103307	−	1.05855i
$863$			1246.70i			1.44461i	0.691573	+	0.722306i	$0.256918\pi$
$863$			1246.70i			1.44461i	−0.691573	+	0.722306i	$0.743082\pi$
$864$		0			0
$865$	−268.006			−0.309833
$866$	−560.983	+	54.7483i	−0.647786	+	0.0632197i
$867$		0			0
$868$	−18.1127	+	3.56936i	−0.0208672	+	0.00411216i
$869$	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	−0.541318	−	0.840818i	$-0.682074\pi$
$877$	−73.4991	+	42.4347i	−0.0838074	+	0.0483862i	0.457511	+	0.889204i	$0.348741\pi$
$878$	−311.232	−	141.351i	−0.354479	−	0.160992i
$879$		0			0
$880$	−200.565	−	489.120i	−0.227914	−	0.555818i
$881$	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	$0.607848\pi$
$884$	109.953	−	96.0803i	0.124381	−	0.108688i
$885$		0			0
$886$	24.3095	−	53.5255i	0.0274374	−	0.0604126i
$887$	−955.774	+	551.816i	−1.07754	+	0.622115i	−0.930230	−	0.366976i	$-0.880393\pi$
$887$	−955.774	+	551.816i	−1.07754	+	0.622115i	−0.147305	+	0.989091i	$0.547060\pi$
$888$		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
$896$	−102.813	+	16.3176i	−0.114747	+	0.0182116i
$897$		0			0
$898$	−848.238	+	82.7825i	−0.944586	+	0.0921854i
$899$	−176.710			−0.196563
$900$		0			0
$901$		−	148.569i		−	0.164894i
$902$	−81.1710	+	7.92176i	−0.0899900	+	0.00878244i
$903$		0			0
$904$	−826.830	−	778.562i	−0.914635	−	0.861241i
$905$	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	0.244643	−	0.969613i	$-0.421329\pi$
$911$	−430.671	−	248.648i	−0.472746	−	0.272940i	−0.717388	+	0.696673i	$0.754663\pi$
$912$		0			0
$913$	−26.2848	−	45.5266i	−0.0287895	−	0.0498649i
$914$	−295.258	+	650.110i	−0.323040	+	0.711280i
$915$		0			0
$916$	322.691	−	281.978i	0.352282	−	0.307837i
$917$			126.408i			0.137850i
$918$		0			0
$919$			222.255i			0.241845i	0.992662	+	0.120922i	$0.0385852\pi$
$919$			222.255i			0.241845i	−0.992662	+	0.120922i	$0.961415\pi$
$920$	−60.7612	+	257.482i	−0.0660448	+	0.279872i
$921$		0			0
$922$	1522.66	+	691.542i	1.65148	+	0.750046i
$923$	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
$932$	882.724	−	173.953i	0.947129	−	0.186645i
$933$		0			0
$934$	−440.342	+	42.9745i	−0.471459	+	0.0460113i
$935$			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	$0.498683\pi$
$938$	−3.13378	−	32.1105i	−0.00334091	−	0.0342330i
$939$		0			0
$940$	−1431.28	+	282.054i	−1.52264	+	0.300058i
$941$	407.216	−	235.106i	0.432748	−	0.249847i	−0.267768	−	0.963483i	$-0.586286\pi$
$941$	407.216	−	235.106i	0.432748	−	0.249847i	0.700517	+	0.713636i	$0.252953\pi$
$942$		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
$950$	−138.846	+	305.717i	−0.146154	+	0.321807i
$951$		0			0
$952$	11.0635	+	2.61080i	0.0116214	+	0.00274244i
$953$	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
$956$	−269.206	+	235.241i	−0.281596	+	0.246068i
$957$		0			0
$958$	1043.68	+	474.004i	1.08943	+	0.494785i
$959$	−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	$-0.326977\pi$
$967$	1466.93	−	846.934i	1.51699	−	0.875836i	0.999801	−	0.0199668i	$-0.00635606\pi$
$968$	382.307	+	359.989i	0.394945	+	0.371890i
$969$		0			0
$970$	−16.1973	−	165.967i	−0.0166983	−	0.171100i
$971$	−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
$974$	−76.1335	−	780.109i	−0.0781659	−	0.800933i
$975$		0			0
$976$	−1118.84	−	151.350i	−1.14636	−	0.155071i
$977$	−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	0.812824	−	0.582509i	$-0.197929\pi$
$983$	702.617	+	405.656i	0.714768	+	0.412672i	−0.0980558	+	0.995181i	$0.531262\pi$
$984$		0			0
$985$	−343.053	−	594.185i	−0.348277	−	0.603234i
$986$	99.0707	+	44.9946i	0.100477	+	0.0456335i
$987$		0			0
$988$	−2000.74	+	1748.32i	−2.02504	+	1.76955i
$989$		−	333.300i		−	0.337007i
$990$		0			0
$991$		−	1111.56i		−	1.12166i	−0.827931	−	0.560829i	$-0.810482\pi$
$991$		−	1111.56i		−	1.12166i	0.827931	−	0.560829i	$-0.189518\pi$
$992$	96.5798	−	153.784i	0.0973586	−	0.155024i
$993$		0			0
$994$	−46.6203	+	102.650i	−0.0469017	+	0.103270i
$995$	−596.021	−	1032.34i	−0.599016	−	1.03753i
$996$		0			0
$997$	1017.90	+	587.682i	1.02096	+	0.589451i	0.914381	−	0.404854i	$-0.132678\pi$
$997$	1017.90	+	587.682i	1.02096	+	0.589451i	0.106577	+	0.994304i	$0.466011\pi$
$998$	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.19.20		40
3.2	odd	2		72.3.p.b.43.1	✓	40
4.3	odd	2		864.3.t.b.559.14		40
8.3	odd	2	inner	216.3.p.b.19.7		40
8.5	even	2		864.3.t.b.559.7		40
9.2	odd	6		648.3.b.f.163.14		20
9.4	even	3	inner	216.3.p.b.91.7		40
9.5	odd	6		72.3.p.b.67.14	yes	40
9.7	even	3		648.3.b.e.163.7		20
12.11	even	2		288.3.t.b.79.11		40
24.5	odd	2		288.3.t.b.79.12		40
24.11	even	2		72.3.p.b.43.14	yes	40
36.7	odd	6		2592.3.b.f.1135.14		20
36.11	even	6		2592.3.b.e.1135.7		20
36.23	even	6		288.3.t.b.175.12		40
36.31	odd	6		864.3.t.b.847.7		40
72.5	odd	6		288.3.t.b.175.11		40
72.11	even	6		648.3.b.f.163.13		20
72.13	even	6		864.3.t.b.847.14		40
72.29	odd	6		2592.3.b.e.1135.14		20
72.43	odd	6		648.3.b.e.163.8		20
72.59	even	6		72.3.p.b.67.1	yes	40
72.61	even	6		2592.3.b.f.1135.7		20
72.67	odd	6	inner	216.3.p.b.91.20		40

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

\(f(q)\)	\(=\)	\(q+(1.99054 - 0.194264i) q^{2} +(3.92452 - 0.773382i) q^{4} +(3.84571 - 2.22032i) q^{5} +(-0.704321 - 0.406640i) q^{7} +(7.66169 - 2.30184i) q^{8} +O(q^{10})\)	\(q+(1.99054 - 0.194264i) q^{2} +(3.92452 - 0.773382i) q^{4} +(3.84571 - 2.22032i) q^{5} +(-0.704321 - 0.406640i) q^{7} +(7.66169 - 2.30184i) q^{8} +(7.22371 - 5.16672i) q^{10} +(3.72022 - 6.44360i) q^{11} +(-18.0943 + 10.4468i) q^{13} +(-1.48098 - 0.672610i) q^{14} +(14.8038 - 6.07031i) q^{16} -1.74716 q^{17} +31.7920 q^{19} +(13.3754 - 11.6879i) q^{20} +(6.15349 - 13.5490i) q^{22} +(-6.44927 + 3.72348i) q^{23} +(-2.64036 + 4.57325i) q^{25} +(-33.9881 + 24.3098i) q^{26} +(-3.07861 - 1.05116i) q^{28} +(-26.9672 - 15.5695i) q^{29} +(4.91458 - 2.83744i) q^{31} +(28.2883 - 14.9590i) q^{32} +(-3.47779 + 0.339410i) q^{34} -3.61148 q^{35} +62.0787i q^{37} +(63.2833 - 6.17604i) q^{38} +(24.3538 - 25.8636i) q^{40} +(-2.74032 - 4.74637i) q^{41} +(-22.3782 + 38.7602i) q^{43} +(9.61671 - 28.1652i) q^{44} +(-12.1142 + 8.66462i) q^{46} +(-71.1253 - 41.0642i) q^{47} +(-24.1693 - 41.8624i) q^{49} +(-4.36734 + 9.61617i) q^{50} +(-62.9323 + 54.9924i) q^{52} +85.0348i q^{53} -33.0403i q^{55} +(-6.33232 - 1.49431i) q^{56} +(-56.7040 - 25.7530i) q^{58} +(21.8641 + 37.8697i) q^{59} +(-61.1107 - 35.2823i) q^{61} +(9.23148 - 6.60276i) q^{62} +(53.4030 - 35.2720i) q^{64} +(-46.3903 + 80.3504i) q^{65} +(9.91758 + 17.1778i) q^{67} +(-6.85675 + 1.35122i) q^{68} +(-7.18881 + 0.701581i) q^{70} -69.3125i q^{71} -21.7177 q^{73} +(12.0597 + 123.570i) q^{74} +(124.768 - 24.5873i) q^{76} +(-5.24046 + 3.02558i) q^{77} +(37.1475 + 21.4471i) q^{79} +(43.4529 - 56.2137i) q^{80} +(-6.37677 - 8.91551i) q^{82} +(3.53270 - 6.11881i) q^{83} +(-6.71905 + 3.87924i) q^{85} +(-37.0151 + 81.5012i) q^{86} +(13.6710 - 57.9323i) q^{88} -37.1192 q^{89} +16.9923 q^{91} +(-22.4306 + 19.6006i) q^{92} +(-149.555 - 67.9230i) q^{94} +(122.263 - 70.5883i) q^{95} +(9.38806 - 16.2606i) q^{97} +(-56.2424 - 78.6338i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 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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