LMFDB - Embedded newform 108.4.h.b.35.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	108.35
Dual form			108.4.h.b.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +O(q^{10})$	\(q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +(43.1673 + 19.4137i) q^{10} +(2.44092 - 4.22780i) q^{11} +(6.03848 + 10.4590i) q^{13} +(5.50343 + 54.3211i) q^{14} +(-51.2068 - 38.3909i) q^{16} +71.2528i q^{17} +68.3003i q^{19} +(26.8509 + 131.154i) q^{20} +(13.7376 - 1.39180i) q^{22} +(-68.0491 - 117.865i) q^{23} +(77.5192 - 134.267i) q^{25} +(-14.0106 + 31.1533i) q^{26} +(-115.536 + 102.470i) q^{28} +(-190.237 - 109.833i) q^{29} +(285.221 - 164.672i) q^{31} +(3.39507 - 180.987i) q^{32} +(-163.487 + 117.846i) q^{34} +323.035 q^{35} -133.618 q^{37} +(-156.713 + 112.963i) q^{38} +(-256.520 + 278.526i) q^{40} +(29.5326 - 17.0507i) q^{41} +(0.558209 + 0.322282i) q^{43} +(25.9142 + 29.2186i) q^{44} +(157.889 - 351.074i) q^{46} +(93.4753 - 161.904i) q^{47} +(14.8169 + 25.6636i) q^{49} +(436.282 - 44.2010i) q^{50} +(-94.6525 + 19.3780i) q^{52} -266.453i q^{53} -81.6944i q^{55} +(-426.199 - 95.6168i) q^{56} +(-62.6263 - 618.147i) q^{58} +(-104.347 - 180.734i) q^{59} +(0.801886 - 1.38891i) q^{61} +(849.565 + 382.076i) q^{62} +(420.885 - 291.548i) q^{64} +(175.024 + 101.050i) q^{65} +(-371.407 + 214.432i) q^{67} +(-540.787 - 180.209i) q^{68} +(534.272 + 741.193i) q^{70} -386.365 q^{71} -776.832 q^{73} +(-220.992 - 306.582i) q^{74} +(-518.378 - 172.742i) q^{76} +(81.6122 - 47.1188i) q^{77} +(-68.5000 - 39.5485i) q^{79} +(-1063.33 - 127.919i) q^{80} +(87.9665 + 39.5613i) q^{82} +(-462.668 + 801.365i) q^{83} +(596.185 + 1032.62i) q^{85} +(0.183763 + 1.81382i) q^{86} +(-24.1811 + 107.784i) q^{88} +1044.26i q^{89} +233.130i q^{91} +(1066.66 - 218.375i) q^{92} +(526.083 - 53.2991i) q^{94} +(571.481 + 989.834i) q^{95} +(733.184 - 1269.91i) q^{97} +(-34.3784 + 76.4422i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.65391	+	2.29447i	0.584746	+	0.811216i
$2$	1.65391	+	2.29447i	0.584746	+	0.811216i
$3$		0			0
$3$		0			0
$4$	−2.52915	+	7.58969i	−0.316144	+	0.948711i
$5$	14.4924	−	8.36717i	1.29624	−	0.748383i	0.316485	−	0.948598i	$-0.397497\pi$
$5$	14.4924	−	8.36717i	1.29624	−	0.748383i	0.979752	+	0.200215i	$0.0641640\pi$
$6$		0			0
$7$	16.7175	+	9.65186i	0.902661	+	0.521152i	0.878063	−	0.478546i	$-0.158836\pi$
$7$	16.7175	+	9.65186i	0.902661	+	0.521152i	0.0245984	+	0.999697i	$0.492169\pi$
$8$	−21.5973	+	6.74964i	−0.954474	+	0.298295i
$9$		0			0
$10$	43.1673	+	19.4137i	1.36507	+	0.613915i
$11$	2.44092	−	4.22780i	0.0669059	−	0.115884i	−0.830632	−	0.556822i	$-0.812021\pi$
$11$	2.44092	−	4.22780i	0.0669059	−	0.115884i	0.897538	+	0.440937i	$0.145354\pi$
$12$		0			0
$13$	6.03848	+	10.4590i	0.128829	+	0.223138i	0.923223	−	0.384264i	$-0.125545\pi$
$13$	6.03848	+	10.4590i	0.128829	+	0.223138i	−0.794394	+	0.607402i	$0.792212\pi$
$14$	5.50343	+	54.3211i	0.105061	+	1.03699i
$15$		0			0
$16$	−51.2068	−	38.3909i	−0.800106	−	0.599858i
$17$			71.2528i			1.01655i	0.861195	+	0.508275i	$0.169717\pi$
$17$			71.2528i			1.01655i	−0.861195	+	0.508275i	$0.830283\pi$
$18$		0			0
$19$			68.3003i			0.824693i	0.911027	+	0.412347i	$0.135291\pi$
$19$			68.3003i			0.824693i	−0.911027	+	0.412347i	$0.864709\pi$
$20$	26.8509	+	131.154i	0.300202	+	1.46635i
$21$		0			0
$22$	13.7376	−	1.39180i	0.133130	−	0.0134878i
$23$	−68.0491	−	117.865i	−0.616923	−	1.06854i	−0.990044	−	0.140759i	$-0.955046\pi$
$23$	−68.0491	−	117.865i	−0.616923	−	1.06854i	0.373121	−	0.927783i	$-0.378288\pi$
$24$		0			0
$25$	77.5192	−	134.267i	0.620154	−	1.07414i
$26$	−14.0106	+	31.1533i	−0.105681	+	0.234987i
$27$		0			0
$28$	−115.536	+	102.470i	−0.779793	+	0.691606i
$29$	−190.237	−	109.833i	−1.21814	−	0.703295i	−0.253622	−	0.967303i	$-0.581622\pi$
$29$	−190.237	−	109.833i	−1.21814	−	0.703295i	−0.964520	+	0.264009i	$0.914955\pi$
$30$		0			0
$31$	285.221	−	164.672i	1.65249	−	0.954065i	0.676444	−	0.736494i	$-0.263520\pi$
$31$	285.221	−	164.672i	1.65249	−	0.954065i	0.976044	−	0.217571i	$-0.0698134\pi$
$32$	3.39507	−	180.987i	0.0187553	−	0.999824i
$33$		0			0
$34$	−163.487	+	117.846i	−0.824642	+	0.594424i
$35$	323.035			1.56008
$36$		0			0
$37$	−133.618			−0.593693			−0.296847	−	0.954925i	$-0.595935\pi$
$37$	−133.618			−0.593693			−0.296847	+	0.954925i	$0.595935\pi$
$38$	−156.713	+	112.963i	−0.669005	+	0.482236i
$39$		0			0
$40$	−256.520	+	278.526i	−1.01399	+	1.10097i
$41$	29.5326	−	17.0507i	0.112493	−	0.0649480i	−0.442698	−	0.896671i	$-0.645979\pi$
$41$	29.5326	−	17.0507i	0.112493	−	0.0649480i	0.555191	+	0.831723i	$0.312645\pi$
$42$		0			0
$43$	0.558209	+	0.322282i	0.00197967	+	0.00114297i	0.500990	−	0.865453i	$-0.332970\pi$
$43$	0.558209	+	0.322282i	0.00197967	+	0.00114297i	−0.499010	+	0.866596i	$0.666303\pi$
$44$	25.9142	+	29.2186i	0.0887890	+	0.100111i
$45$		0			0
$46$	157.889	−	351.074i	0.506075	−	1.12528i
$47$	93.4753	−	161.904i	0.290102	−	0.502471i	−0.683732	−	0.729733i	$-0.739644\pi$
$47$	93.4753	−	161.904i	0.290102	−	0.502471i	0.973834	+	0.227263i	$0.0729775\pi$
$48$		0			0
$49$	14.8169	+	25.6636i	0.0431979	+	0.0748210i
$50$	436.282	−	44.2010i	1.23399	−	0.125019i
$51$		0			0
$52$	−94.6525	+	19.3780i	−0.252422	+	0.0516777i
$53$		−	266.453i		−	0.690569i	−0.938498	−	0.345284i	$-0.887782\pi$
$53$		−	266.453i		−	0.690569i	0.938498	−	0.345284i	$-0.112218\pi$
$54$		0			0
$55$		−	81.6944i		−	0.200285i
$56$	−426.199	−	95.6168i	−1.01702	−	0.228167i
$57$		0			0
$58$	−62.6263	−	618.147i	−0.141780	−	1.39943i
$59$	−104.347	−	180.734i	−0.230251	−	0.398806i	0.727631	−	0.685969i	$-0.240621\pi$
$59$	−104.347	−	180.734i	−0.230251	−	0.398806i	−0.957882	+	0.287163i	$0.907288\pi$
$60$		0			0
$61$	0.801886	−	1.38891i	0.00168313	−	0.00291527i	−0.865183	−	0.501457i	$-0.832798\pi$
$61$	0.801886	−	1.38891i	0.00168313	−	0.00291527i	0.866866	+	0.498542i	$0.166131\pi$
$62$	849.565	+	382.076i	1.74024	+	0.782640i
$63$		0			0
$64$	420.885	−	291.548i	0.822041	−	0.569429i
$65$	175.024	+	101.050i	0.333985	+	0.192826i
$66$		0			0
$67$	−371.407	+	214.432i	−0.677233	+	0.391001i	−0.798812	−	0.601581i	$-0.794538\pi$
$67$	−371.407	+	214.432i	−0.677233	+	0.391001i	0.121579	+	0.992582i	$0.461204\pi$
$68$	−540.787	−	180.209i	−0.964412	−	0.321376i
$69$		0			0
$70$	534.272	+	741.193i	0.912253	+	1.26557i
$71$	−386.365			−0.645817			−0.322909	−	0.946430i	$-0.604661\pi$
$71$	−386.365			−0.645817			−0.322909	+	0.946430i	$0.604661\pi$
$72$		0			0
$73$	−776.832			−1.24550			−0.622749	−	0.782422i	$-0.713984\pi$
$73$	−776.832			−1.24550			−0.622749	+	0.782422i	$0.713984\pi$
$74$	−220.992	−	306.582i	−0.347160	−	0.481614i
$75$		0			0
$76$	−518.378	−	172.742i	−0.782396	−	0.260721i
$77$	81.6122	−	47.1188i	0.120787	−	0.0697362i
$78$		0			0
$79$	−68.5000	−	39.5485i	−0.0975551	−	0.0563235i	0.450429	−	0.892812i	$-0.351271\pi$
$79$	−68.5000	−	39.5485i	−0.0975551	−	0.0563235i	−0.547984	+	0.836489i	$0.684604\pi$
$80$	−1063.33	−	127.919i	−1.48605	−	0.178772i
$81$		0			0
$82$	87.9665	+	39.5613i	0.118467	+	0.0532782i
$83$	−462.668	+	801.365i	−0.611861	+	1.05977i	0.379066	+	0.925370i	$0.376245\pi$
$83$	−462.668	+	801.365i	−0.611861	+	1.05977i	−0.990927	+	0.134404i	$0.957088\pi$
$84$		0			0
$85$	596.185	+	1032.62i	0.760768	+	1.31769i
$86$	0.183763	+	1.81382i	0.000230415	+	0.00227429i
$87$		0			0
$88$	−24.1811	+	107.784i	−0.0292922	+	0.130566i
$89$			1044.26i			1.24372i	0.783128	+	0.621861i	$0.213623\pi$
$89$			1044.26i			1.24372i	−0.783128	+	0.621861i	$0.786377\pi$
$90$		0			0
$91$			233.130i			0.268557i
$92$	1066.66	−	218.375i	1.20877	−	0.247469i
$93$		0			0
$94$	526.083	−	53.2991i	0.577248	−	0.0584828i
$95$	571.481	+	989.834i	0.617186	+	1.06900i
$96$		0			0
$97$	733.184	−	1269.91i	0.767460	−	1.32928i	−0.171477	−	0.985188i	$-0.554854\pi$
$97$	733.184	−	1269.91i	0.767460	−	1.32928i	0.938936	−	0.344091i	$-0.111813\pi$
$98$	−34.3784	+	76.4422i	−0.0354362	+	0.0787941i
$99$		0			0
$100$	822.989	+	927.929i	0.822989	+	0.927929i
$101$	314.302	+	181.462i	0.309646	+	0.178774i	0.646768	−	0.762687i	$-0.276120\pi$
$101$	314.302	+	181.462i	0.309646	+	0.178774i	−0.337122	+	0.941461i	$0.609454\pi$
$102$		0			0
$103$	−466.128	+	269.119i	−0.445912	+	0.257447i	−0.706102	−	0.708110i	$-0.749548\pi$
$103$	−466.128	+	269.119i	−0.445912	+	0.257447i	0.260190	+	0.965557i	$0.416215\pi$
$104$	−201.009	−	185.127i	−0.189525	−	0.174550i
$105$		0			0
$106$	611.368	−	440.690i	0.560201	−	0.403808i
$107$	−430.456			−0.388914			−0.194457	−	0.980911i	$-0.562294\pi$
$107$	−430.456			−0.388914			−0.194457	+	0.980911i	$0.562294\pi$
$108$		0			0
$109$	899.324			0.790272			0.395136	−	0.918623i	$-0.370697\pi$
$109$	899.324			0.790272			0.395136	+	0.918623i	$0.370697\pi$
$110$	187.445	−	135.115i	0.162474	−	0.117116i
$111$		0			0
$112$	−485.507	−	1136.04i	−0.409608	−	0.958445i
$113$	330.860	−	191.022i	0.275440	−	0.159025i	−0.355917	−	0.934517i	$-0.615832\pi$
$113$	330.860	−	191.022i	0.275440	−	0.159025i	0.631357	+	0.775492i	$0.282498\pi$
$114$		0			0
$115$	−1972.39	−	1138.76i	−1.59936	−	0.923389i
$116$	1314.74	−	1166.05i	1.05233	−	0.933323i
$117$		0			0
$118$	242.107	−	538.338i	0.188880	−	0.419983i
$119$	−687.722	+	1191.17i	−0.529776	+	0.917600i
$120$		0			0
$121$	653.584	+	1132.04i	0.491047	+	0.850519i
$122$	4.51305	−	0.457231i	0.00334912	−	0.000339309i
$123$		0			0
$124$	528.446	+	2581.22i	0.382708	+	1.86936i
$125$		−	502.674i		−	0.359684i
$126$		0			0
$127$			1677.92i			1.17237i	0.810177	+	0.586186i	$0.199371\pi$
$127$			1677.92i			1.17237i	−0.810177	+	0.586186i	$0.800629\pi$
$128$	1365.05	+	483.512i	0.942615	+	0.333881i
$129$		0			0
$130$	57.6181	+	568.714i	0.0388727	+	0.383689i
$131$	−712.418	−	1233.94i	−0.475147	−	0.822979i	0.524448	−	0.851443i	$-0.324272\pi$
$131$	−712.418	−	1233.94i	−0.475147	−	0.822979i	−0.999595	+	0.0284637i	$0.990938\pi$
$132$		0			0
$133$	−659.225	+	1141.81i	−0.429790	+	0.744418i
$134$	−1106.28	−	497.529i	−0.713196	−	0.320746i
$135$		0			0
$136$	−480.931	−	1538.87i	−0.303231	−	0.970270i
$137$	−23.2295	−	13.4116i	−0.0144864	−	0.00836370i	0.492739	−	0.870177i	$-0.335996\pi$
$137$	−23.2295	−	13.4116i	−0.0144864	−	0.00836370i	−0.507226	+	0.861813i	$0.669329\pi$
$138$		0			0
$139$	1434.57	−	828.252i	0.875388	−	0.505406i	0.00625321	−	0.999980i	$-0.498010\pi$
$139$	1434.57	−	828.252i	0.875388	−	0.505406i	0.869135	+	0.494575i	$0.164676\pi$
$140$	−817.004	+	2451.74i	−0.493210	+	1.48007i
$141$		0			0
$142$	−639.013	−	886.500i	−0.377639	−	0.523898i
$143$	58.9578			0.0344776
$144$		0			0
$145$	−3675.98			−2.10533
$146$	−1284.81	−	1782.42i	−0.728300	−	1.01037i
$147$		0			0
$148$	337.940	−	1014.12i	0.187692	−	0.563244i
$149$	−738.285	+	426.249i	−0.405924	+	0.234360i	−0.689037	−	0.724726i	$-0.741966\pi$
$149$	−738.285	+	426.249i	−0.405924	+	0.234360i	0.283113	+	0.959087i	$0.408633\pi$
$150$		0			0
$151$	1272.06	+	734.422i	0.685553	+	0.395804i	0.801944	−	0.597399i	$-0.203799\pi$
$151$	1272.06	+	734.422i	0.685553	+	0.395804i	−0.116391	+	0.993203i	$0.537133\pi$
$152$	−461.002	−	1475.10i	−0.246002	−	0.787148i
$153$		0			0
$154$	243.092	+	109.326i	0.127201	+	0.0572061i
$155$	2755.68	−	4772.98i	1.42801	−	2.47339i
$156$		0			0
$157$	−1344.52	−	2328.78i	−0.683469	−	1.18380i	−0.973915	−	0.226912i	$-0.927137\pi$
$157$	−1344.52	−	2328.78i	−0.683469	−	1.18380i	0.290446	−	0.956891i	$-0.406196\pi$
$158$	−22.5503	−	222.581i	−0.0113545	−	0.112073i
$159$		0			0
$160$	−1465.15	−	2651.35i	−0.723940	−	1.31005i
$161$		−	2627.20i		−	1.28604i
$162$		0			0
$163$		−	2186.50i		−	1.05067i	−0.850895	−	0.525336i	$-0.823940\pi$
$163$		−	2186.50i		−	1.05067i	0.850895	−	0.525336i	$-0.176060\pi$
$164$	54.7169	+	267.267i	0.0260529	+	0.127256i
$165$		0			0
$166$	−2603.92	+	263.811i	−1.21749	+	0.123348i
$167$	1790.65	+	3101.49i	0.829726	+	1.43713i	0.898253	+	0.439479i	$0.144837\pi$
$167$	1790.65	+	3101.49i	0.829726	+	1.43713i	−0.0685268	+	0.997649i	$0.521830\pi$
$168$		0			0
$169$	1025.57	−	1776.35i	0.466806	−	0.808532i
$170$	−1383.28	+	3075.79i	−0.624075	+	1.38766i
$171$		0			0
$172$	−3.85781	+	3.42153i	−0.00171021	+	0.00151680i
$173$	94.5051	+	54.5625i	0.0415323	+	0.0239787i	0.520622	−	0.853787i	$-0.325700\pi$
$173$	94.5051	+	54.5625i	0.0415323	+	0.0239787i	−0.479090	+	0.877766i	$0.659033\pi$
$174$		0			0
$175$	2591.86	−	1496.41i	1.11958	−	0.646388i
$176$	−287.301	+	122.783i	−0.123046	+	0.0525858i
$177$		0			0
$178$	−2396.02	+	1727.11i	−1.00893	+	0.727262i
$179$	−268.397			−0.112072			−0.0560361	−	0.998429i	$-0.517846\pi$
$179$	−268.397			−0.112072			−0.0560361	+	0.998429i	$0.517846\pi$
$180$		0			0
$181$	898.582			0.369011			0.184506	−	0.982831i	$-0.440932\pi$
$181$	898.582			0.369011			0.184506	+	0.982831i	$0.440932\pi$
$182$	−534.910	+	385.577i	−0.217858	+	0.157038i
$183$		0			0
$184$	2265.22	+	2086.25i	0.907577	+	0.835870i
$185$	−1936.44	+	1118.00i	−0.769567	+	0.444310i
$186$		0			0
$187$	301.242	+	173.922i	0.117802	+	0.0680132i
$188$	992.388	+	1118.93i	0.384986	+	0.434076i
$189$		0			0
$190$	−1325.96	+	2948.34i	−0.506291	+	1.12576i
$191$	257.331	−	445.711i	0.0974860	−	0.168851i	−0.813157	−	0.582044i	$-0.802253\pi$
$191$	257.331	−	445.711i	0.0974860	−	0.168851i	0.910643	+	0.413193i	$0.135587\pi$
$192$		0			0
$193$	1229.66	+	2129.83i	0.458616	+	0.794346i	0.998888	−	0.0471443i	$-0.0150121\pi$
$193$	1229.66	+	2129.83i	0.458616	+	0.794346i	−0.540272	+	0.841490i	$0.681679\pi$
$194$	4126.39	−	418.057i	1.52710	−	0.154715i
$195$		0			0
$196$	−232.253	+	47.5485i	−0.0846403	+	0.0173282i
$197$		−	646.506i		−	0.233815i	−0.993143	−	0.116908i	$-0.962702\pi$
$197$		−	646.506i		−	0.233815i	0.993143	−	0.116908i	$-0.0372982\pi$
$198$		0			0
$199$			1742.98i			0.620886i	0.950592	+	0.310443i	$0.100477\pi$
$199$			1742.98i			0.620886i	−0.950592	+	0.310443i	$0.899523\pi$
$200$	−767.949	+	3423.03i	−0.271511	+	1.21022i
$201$		0			0
$202$	103.469	+	1021.28i	0.0360398	+	0.355727i
$203$	−2120.19	−	3672.28i	−0.733046	−	1.26967i
$204$		0			0
$205$	285.332	−	494.209i	0.0972119	−	0.168376i
$206$	−1388.42	−	624.415i	−0.469591	−	0.211190i
$207$		0			0
$208$	92.3175	−	767.393i	0.0307744	−	0.255813i
$209$	288.760	+	166.716i	0.0955691	+	0.0551769i
$210$		0			0
$211$	−3648.27	+	2106.33i	−1.19032	+	0.687231i	−0.958379	−	0.285499i	$-0.907841\pi$
$211$	−3648.27	+	2106.33i	−1.19032	+	0.687231i	−0.231940	+	0.972730i	$0.574507\pi$
$212$	2022.30	+	673.900i	0.655151	+	0.218319i
$213$		0			0
$214$	−711.937	−	987.667i	−0.227416	−	0.315493i
$215$	10.7864			0.00342150
$216$		0			0
$217$	6357.58			1.98885
$218$	1487.40	+	2063.47i	0.462109	+	0.641081i
$219$		0			0
$220$	620.035	+	206.617i	0.190013	+	0.0633188i
$221$	−745.230	+	430.259i	−0.226831	+	0.130961i
$222$		0			0
$223$	5558.55	+	3209.23i	1.66918	+	0.963703i	0.968080	+	0.250643i	$0.0806420\pi$
$223$	5558.55	+	3209.23i	1.66918	+	0.963703i	0.701103	+	0.713060i	$0.252691\pi$
$224$	1803.62	−	2992.89i	0.537990	−	0.892728i
$225$		0			0
$226$	985.507	+	443.213i	0.290066	+	0.130452i
$227$	−1124.83	+	1948.27i	−0.328889	+	0.569653i	−0.982292	−	0.187358i	$-0.940008\pi$
$227$	−1124.83	+	1948.27i	−0.328889	+	0.569653i	0.653403	+	0.757011i	$0.273341\pi$
$228$		0			0
$229$	−1735.36	−	3005.74i	−0.500769	−	0.867357i	−1.00000		0.000888202i	$-0.999717\pi$
$229$	−1735.36	−	3005.74i	−0.500769	−	0.867357i	0.499231	−	0.866469i	$-0.333616\pi$
$230$	−649.313	−	6408.98i	−0.186150	−	1.83737i
$231$		0			0
$232$	4849.94	+	1088.07i	1.37247	+	0.307911i
$233$			3852.67i			1.08325i	0.840621	+	0.541624i	$0.182190\pi$
$233$			3852.67i			1.08325i	−0.840621	+	0.541624i	$0.817810\pi$
$234$		0			0
$235$		−	3128.50i		−	0.868428i
$236$	1635.62	−	334.857i	0.451144	−	0.0923615i
$237$		0			0
$238$	−3870.53	+	392.135i	−1.05416	+	0.106800i
$239$	19.9334	+	34.5257i	0.00539491	+	0.00934426i	0.868710	−	0.495321i	$-0.164949\pi$
$239$	19.9334	+	34.5257i	0.00539491	+	0.00934426i	−0.863315	+	0.504665i	$0.831616\pi$
$240$		0			0
$241$	−1729.18	+	2995.03i	−0.462184	+	0.800527i	−0.999070	−	0.0431286i	$-0.986267\pi$
$241$	−1729.18	+	2995.03i	−0.462184	+	0.800527i	0.536885	+	0.843655i	$0.319601\pi$
$242$	−1516.46	+	3371.92i	−0.402817	+	0.895683i
$243$		0			0
$244$	8.51329	+	9.59882i	0.00223364	+	0.00251845i
$245$	429.464	+	247.951i	0.111989	+	0.0646572i
$246$		0			0
$247$	−714.350	+	412.430i	−0.184020	+	0.106244i
$248$	−5048.51	+	5481.61i	−1.29267	+	1.40356i
$249$		0			0
$250$	1153.37	−	831.378i	0.291781	−	0.210324i
$251$	2977.61			0.748786			0.374393	−	0.927270i	$-0.377851\pi$
$251$	2977.61			0.748786			0.374393	+	0.927270i	$0.377851\pi$
$252$		0			0
$253$	−664.410			−0.165103
$254$	−3849.93	+	2775.13i	−0.951047	+	0.685540i
$255$		0			0
$256$	1148.28	+	3931.75i	0.280341	+	0.959901i
$257$	5593.28	−	3229.28i	1.35758	−	0.783802i	0.368287	−	0.929712i	$-0.379944\pi$
$257$	5593.28	−	3229.28i	1.35758	−	0.783802i	0.989298	+	0.145910i	$0.0466111\pi$
$258$		0			0
$259$	−2233.76	−	1289.66i	−0.535904	−	0.309404i
$260$	−1209.60	+	1072.81i	−0.288524	+	0.255895i
$261$		0			0
$262$	1652.97	−	3675.46i	0.389773	−	0.866681i
$263$	−2940.99	+	5093.94i	−0.689540	+	1.19432i	0.282447	+	0.959283i	$0.408854\pi$
$263$	−2940.99	+	5093.94i	−0.689540	+	1.19432i	−0.971987	+	0.235036i	$0.924479\pi$
$264$		0			0
$265$	−2229.46	−	3861.54i	−0.516810	−	0.895141i
$266$	−3710.15	+	375.886i	−0.855203	+	0.0866431i
$267$		0			0
$268$	−688.129	−	3361.20i	−0.156844	−	0.766111i
$269$			2967.07i			0.672510i	0.941771	+	0.336255i	$0.109160\pi$
$269$			2967.07i			0.672510i	−0.941771	+	0.336255i	$0.890840\pi$
$270$		0			0
$271$		−	1985.78i		−	0.445121i	−0.974919	−	0.222561i	$-0.928559\pi$
$271$		−	1985.78i		−	0.445121i	0.974919	−	0.222561i	$-0.0714415\pi$
$272$	2735.46	−	3648.63i	0.609785	−	0.813348i
$273$		0			0
$274$	−7.64719	−	75.4808i	−0.00168607	−	0.0166422i
$275$	−378.436	−	655.471i	−0.0829839	−	0.143732i
$276$		0			0
$277$	−2171.48	+	3761.12i	−0.471017	+	0.815825i	−0.999450	−	0.0331494i	$-0.989446\pi$
$277$	−2171.48	+	3761.12i	−0.471017	+	0.815825i	0.528433	+	0.848975i	$0.322780\pi$
$278$	4273.05	+	1921.73i	0.921873	+	0.414595i
$279$		0			0
$280$	−6976.68	+	2180.37i	−1.48906	+	0.465365i
$281$	−6752.10	−	3898.33i	−1.43344	−	0.827597i	−0.436058	−	0.899919i	$-0.643626\pi$
$281$	−6752.10	−	3898.33i	−1.43344	−	0.827597i	−0.997381	+	0.0723220i	$0.976959\pi$
$282$		0			0
$283$	−1771.47	+	1022.76i	−0.372094	+	0.214829i	−0.674373	−	0.738391i	$-0.735586\pi$
$283$	−1771.47	+	1022.76i	−0.372094	+	0.214829i	0.302279	+	0.953220i	$0.402253\pi$
$284$	977.173	−	2932.39i	0.204171	−	0.612694i
$285$		0			0
$286$	97.5110	+	135.277i	0.0201607	+	0.0279688i
$287$	658.283			0.135391
$288$		0			0
$289$	−163.963			−0.0333732
$290$	−6079.75	−	8434.41i	−1.23109	−	1.70788i
$291$		0			0
$292$	1964.72	−	5895.92i	0.393756	−	1.18162i
$293$	2041.60	−	1178.72i	0.407070	−	0.235022i	−0.282460	−	0.959279i	$-0.591151\pi$
$293$	2041.60	−	1178.72i	0.407070	−	0.235022i	0.689530	+	0.724257i	$0.257817\pi$
$294$		0			0
$295$	−3024.46	−	1746.18i	−0.596919	−	0.344631i
$296$	2885.78	−	901.873i	0.566665	−	0.177096i
$297$		0			0
$298$	−2199.07	−	988.991i	−0.427479	−	0.192251i
$299$	821.827	−	1423.45i	0.158955	−	0.275318i
$300$		0			0
$301$	6.22124	+	10.7755i	0.00119132	+	0.00206342i
$302$	418.763	+	4133.36i	0.0797917	+	0.787576i
$303$		0			0
$304$	2622.11	−	3497.44i	0.494699	−	0.659842i
$305$		−	26.8381i		−	0.00503851i
$306$		0			0
$307$			5521.27i			1.02643i	0.858259	+	0.513217i	$0.171546\pi$
$307$			5521.27i			1.02643i	−0.858259	+	0.513217i	$0.828454\pi$
$308$	151.208	+	738.582i	0.0279736	+	0.136638i
$309$		0			0
$310$	15509.1	−	1571.27i	2.84148	−	0.287879i
$311$	−767.330	−	1329.05i	−0.139908	−	0.242327i	0.787554	−	0.616246i	$-0.211347\pi$
$311$	−767.330	−	1329.05i	−0.139908	−	0.242327i	−0.927461	+	0.373919i	$0.878014\pi$
$312$		0			0
$313$	−4383.28	+	7592.06i	−0.791557	+	1.37102i	0.133446	+	0.991056i	$0.457396\pi$
$313$	−4383.28	+	7592.06i	−0.791557	+	1.37102i	−0.925003	+	0.379961i	$0.875937\pi$
$314$	3119.59	−	6936.57i	0.560664	−	1.24667i
$315$		0			0
$316$	473.408	−	419.870i	0.0842762	−	0.0747454i
$317$	6074.45	+	3507.08i	1.07626	+	0.621380i	0.929886	−	0.367849i	$-0.119906\pi$
$317$	6074.45	+	3507.08i	1.07626	+	0.621380i	0.146376	+	0.989229i	$0.453239\pi$
$318$		0			0
$319$	−928.706	+	536.189i	−0.163002	+	0.0941091i
$320$	3660.19	−	7746.83i	0.639409	−	1.35332i
$321$		0			0
$322$	6028.03	−	4345.16i	1.04326	−	0.752008i
$323$	−4866.59			−0.838342
$324$		0			0
$325$	1872.39			0.319574
$326$	5016.84	−	3616.27i	0.852323	−	0.614377i
$327$		0			0
$328$	−522.738	+	567.582i	−0.0879982	+	0.0955473i
$329$	3125.35	−	1804.42i	0.523727	−	0.302374i
$330$		0			0
$331$	−8563.21	−	4943.97i	−1.42198	−	0.820982i	−0.425515	−	0.904951i	$-0.639907\pi$
$331$	−8563.21	−	4943.97i	−1.42198	−	0.820982i	−0.996468	+	0.0839692i	$0.973240\pi$
$332$	−4911.96	−	5538.28i	−0.811984	−	0.915520i
$333$		0			0
$334$	−4154.69	+	9238.16i	−0.680642	+	1.51344i
$335$	−3588.38	+	6215.26i	−0.585236	+	1.01366i
$336$		0			0
$337$	2504.10	+	4337.22i	0.404768	+	0.701079i	0.994294	−	0.106670i	$-0.0340190\pi$
$337$	2504.10	+	4337.22i	0.404768	+	0.701079i	−0.589527	+	0.807749i	$0.700686\pi$
$338$	5771.97	−	584.776i	0.928858	−	0.0941054i
$339$		0			0
$340$	−9345.12	+	1913.20i	−1.49062	+	0.305170i
$341$		−	1607.81i		−	0.255330i
$342$		0			0
$343$		−	6049.14i		−	0.952252i
$344$	−14.2311	−	3.19271i	−0.00223049	−	0.000500405i
$345$		0			0
$346$	31.1112	+	307.080i	0.00483396	+	0.0477131i
$347$	3897.53	+	6750.72i	0.602969	+	1.04437i	0.992369	+	0.123305i	$0.0393493\pi$
$347$	3897.53	+	6750.72i	0.602969	+	1.04437i	−0.389399	+	0.921069i	$0.627317\pi$
$348$		0			0
$349$	4540.81	−	7864.91i	0.696458	−	1.20630i	−0.273228	−	0.961949i	$-0.588091\pi$
$349$	4540.81	−	7864.91i	0.696458	−	1.20630i	0.969687	−	0.244352i	$-0.0785753\pi$
$350$	7720.17	+	3472.00i	1.17903	+	0.530246i
$351$		0			0
$352$	−756.891	−	456.130i	−0.114609	−	0.0690676i
$353$	−3944.55	−	2277.39i	−0.594752	−	0.343380i	0.172222	−	0.985058i	$-0.444905\pi$
$353$	−3944.55	−	2277.39i	−0.594752	−	0.343380i	−0.766974	+	0.641678i	$0.778239\pi$
$354$		0			0
$355$	−5599.34	+	3232.78i	−0.837133	+	0.483319i
$356$	−7925.61	−	2641.09i	−1.17993	−	0.393195i
$357$		0			0
$358$	−443.905	−	615.828i	−0.0655338	−	0.0909148i
$359$	5415.10			0.796095			0.398047	−	0.917365i	$-0.369688\pi$
$359$	5415.10			0.796095			0.398047	+	0.917365i	$0.369688\pi$
$360$		0			0
$361$	2194.06			0.319881
$362$	1486.18	+	2061.77i	0.215778	+	0.299348i
$363$		0			0
$364$	−1769.39	−	589.621i	−0.254783	−	0.0849026i
$365$	−11258.1	+	6499.89i	−1.61446	+	0.932109i
$366$		0			0
$367$	9228.51	+	5328.08i	1.31260	+	0.757830i	0.982526	−	0.186125i	$-0.0595928\pi$
$367$	9228.51	+	5328.08i	1.31260	+	0.757830i	0.330074	+	0.943955i	$0.392926\pi$
$368$	−1040.35	+	8647.94i	−0.147369	+	1.22501i
$369$		0			0
$370$	−5767.93	−	2594.02i	−0.810433	−	0.364477i
$371$	2571.77	−	4454.43i	0.359891	−	0.623350i
$372$		0			0
$373$	−1354.99	−	2346.91i	−0.188093	−	0.325786i	0.756522	−	0.653969i	$-0.226897\pi$
$373$	−1354.99	−	2346.91i	−0.188093	−	0.325786i	−0.944614	+	0.328183i	$0.893564\pi$
$374$	99.1695	+	978.843i	0.0137111	+	0.135334i
$375$		0			0
$376$	−926.019	+	4127.61i	−0.127010	+	0.566131i
$377$		−	2652.91i		−	0.362418i
$378$		0			0
$379$		−	6395.35i		−	0.866774i	−0.901208	−	0.433387i	$-0.857318\pi$
$379$		−	6395.35i		−	0.866774i	0.901208	−	0.433387i	$-0.142682\pi$
$380$	−8957.89	+	1833.93i	−1.20929	+	0.247575i
$381$		0			0
$382$	1448.27	−	146.729i	0.193979	−	0.0196526i
$383$	−682.579	−	1182.26i	−0.0910656	−	0.157730i	0.816894	−	0.576788i	$-0.195694\pi$
$383$	−682.579	−	1182.26i	−0.0910656	−	0.157730i	−0.907960	+	0.419057i	$0.862361\pi$
$384$		0			0
$385$	788.503	−	1365.73i	0.104379	−	0.180789i
$386$	−2853.08	+	6343.97i	−0.376212	+	0.836528i
$387$		0			0
$388$	7783.91	+	8776.44i	1.01847	+	1.14834i
$389$	5380.83	+	3106.62i	0.701333	+	0.404915i	0.807844	−	0.589397i	$-0.200634\pi$
$389$	5380.83	+	3106.62i	0.701333	+	0.404915i	−0.106510	+	0.994312i	$0.533968\pi$
$390$		0			0
$391$	8398.18	−	4848.69i	1.08623	−	0.627133i
$392$	−493.224	−	454.255i	−0.0635500	−	0.0585290i
$393$		0			0
$394$	1483.39	−	1069.26i	0.189675	−	0.136723i
$395$	−1323.64			−0.168606
$396$		0			0
$397$	3291.69			0.416134			0.208067	−	0.978115i	$-0.433283\pi$
$397$	3291.69			0.416134			0.208067	+	0.978115i	$0.433283\pi$
$398$	−3999.20	+	2882.73i	−0.503672	+	0.363061i
$399$		0			0
$400$	−9124.15	+	3899.36i	−1.14052	+	0.487420i
$401$	−3529.51	+	2037.76i	−0.439539	+	0.253768i	−0.703402	−	0.710792i	$-0.748337\pi$
$401$	−3529.51	+	2037.76i	−0.439539	+	0.253768i	0.263863	+	0.964560i	$0.415003\pi$
$402$		0			0
$403$	3444.60	+	1988.74i	0.425776	+	0.245822i
$404$	−2172.16	+	1926.51i	−0.267498	+	0.237246i
$405$		0			0
$406$	4919.31	−	10938.3i	0.601333	−	1.33710i
$407$	−326.151	+	564.910i	−0.0397216	+	0.0687998i
$408$		0			0
$409$	−7054.78	−	12219.2i	−0.852900	−	1.47727i	−0.878579	−	0.477597i	$-0.841508\pi$
$409$	−7054.78	−	12219.2i	−0.852900	−	1.47727i	0.0256787	−	0.999670i	$-0.491825\pi$
$410$	1605.86	−	162.694i	0.193434	−	0.0195973i
$411$		0			0
$412$	−863.624	−	4218.41i	−0.103271	−	0.504432i
$413$		−	4028.56i		−	0.479982i
$414$		0			0
$415$			15484.9i			1.83162i
$416$	1913.44	−	1057.38i	0.225515	−	0.124621i
$417$		0			0
$418$	95.0603	+	938.283i	0.0111233	+	0.109792i
$419$	−3184.20	−	5515.19i	−0.371261	−	0.643042i	0.618499	−	0.785786i	$-0.287741\pi$
$419$	−3184.20	−	5515.19i	−0.371261	−	0.643042i	−0.989760	+	0.142743i	$0.954408\pi$
$420$		0			0
$421$	−5406.24	+	9363.89i	−0.625853	+	1.08401i	0.362522	+	0.931975i	$0.381916\pi$
$421$	−5406.24	+	9363.89i	−0.625853	+	1.08401i	−0.988375	+	0.152034i	$0.951418\pi$
$422$	−10866.8	−	4887.15i	−1.25353	−	0.563750i
$423$		0			0
$424$	1798.46	+	5754.66i	0.205993	+	0.659130i
$425$	9566.92	+	5523.46i	1.09191	+	0.630417i
$426$		0			0
$427$	26.8111	−	15.4794i	0.00303859	−	0.00175433i
$428$	1088.69	−	3267.03i	0.122953	−	0.368967i
$429$		0			0
$430$	17.8397	+	24.7489i	0.00200071	+	0.00277558i
$431$	−10968.4			−1.22583			−0.612913	−	0.790150i	$-0.710002\pi$
$431$	−10968.4			−1.22583			−0.612913	+	0.790150i	$0.710002\pi$
$432$		0			0
$433$	−1491.10			−0.165491			−0.0827457	−	0.996571i	$-0.526369\pi$
$433$	−1491.10			−0.165491			−0.0827457	+	0.996571i	$0.526369\pi$
$434$	10514.9	+	14587.2i	1.16297	+	1.61339i
$435$		0			0
$436$	−2274.52	+	6825.59i	−0.249839	+	0.749740i
$437$	8050.19	−	4647.78i	0.881219	−	0.508772i
$438$		0			0
$439$	1927.62	+	1112.91i	0.209567	+	0.120994i	0.601110	−	0.799166i	$-0.294725\pi$
$439$	1927.62	+	1112.91i	0.209567	+	0.120994i	−0.391543	+	0.920160i	$0.628059\pi$
$440$	551.408	+	1764.38i	0.0597439	+	0.191167i
$441$		0			0
$442$	−2219.76	−	998.295i	−0.238876	−	0.107430i
$443$	7938.74	−	13750.3i	0.851425	−	1.47471i	−0.0284982	−	0.999594i	$-0.509073\pi$
$443$	7938.74	−	13750.3i	0.851425	−	1.47471i	0.879923	−	0.475117i	$-0.157594\pi$
$444$		0			0
$445$	8737.50	+	15133.8i	0.930780	+	1.61216i
$446$	1829.88	+	18061.7i	0.194277	+	1.91759i
$447$		0			0
$448$	9850.13	−	811.629i	1.03878	−	0.0855934i
$449$			11558.7i			1.21490i	0.794358	+	0.607450i	$0.207807\pi$
$449$			11558.7i			1.21490i	−0.794358	+	0.607450i	$0.792193\pi$
$450$		0			0
$451$		−	166.477i		−	0.0173816i
$452$	613.004	+	2994.25i	0.0637905	+	0.311588i
$453$		0			0
$454$	−6330.61	+	641.373i	−0.654428	+	0.0663021i
$455$	1950.64	+	3378.61i	0.200984	+	0.348114i
$456$		0			0
$457$	5444.85	−	9430.75i	0.557329	−	0.965322i	−0.440390	−	0.897807i	$-0.645160\pi$
$457$	5444.85	−	9430.75i	0.557329	−	0.965322i	0.997718	−	0.0675148i	$-0.0215070\pi$
$458$	4026.43	−	8952.96i	0.410792	−	0.913416i
$459$		0			0
$460$	13631.3	−	12089.7i	1.38166	−	1.22540i
$461$	−10197.5	−	5887.54i	−1.03025	−	0.594816i	−0.113195	−	0.993573i	$-0.536108\pi$
$461$	−10197.5	−	5887.54i	−1.03025	−	0.594816i	−0.917057	+	0.398757i	$0.869442\pi$
$462$		0			0
$463$	−2303.58	+	1329.97i	−0.231223	+	0.133497i	−0.611136	−	0.791525i	$-0.709287\pi$
$463$	−2303.58	+	1329.97i	−0.231223	+	0.133497i	0.379913	+	0.925022i	$0.375954\pi$
$464$	5524.83	+	12927.6i	0.552766	+	1.29342i
$465$		0			0
$466$	−8839.82	+	6371.98i	−0.878749	+	0.633426i
$467$	32.9750			0.00326746			0.00163373	−	0.999999i	$-0.499480\pi$
$467$	32.9750			0.00326746			0.00163373	+	0.999999i	$0.499480\pi$
$468$		0			0
$469$	−8278.68			−0.815083
$470$	7178.23	−	5174.26i	0.704483	−	0.507810i
$471$		0			0
$472$	3473.49	+	3199.06i	0.338730	+	0.311967i
$473$	2.72509	−	1.57333i	0.000264904	−	0.000152942i
$474$		0			0
$475$	9170.50	+	5294.59i	0.885834	+	0.511437i
$476$	−7301.26	−	8232.25i	−0.703052	−	0.792698i
$477$		0			0
$478$	−46.2499	+	102.839i	−0.00442556	+	0.00984046i
$479$	4069.08	−	7047.85i	0.388144	−	0.672284i	−0.604056	−	0.796942i	$-0.706450\pi$
$479$	4069.08	−	7047.85i	0.388144	−	0.672284i	0.992200	+	0.124657i	$0.0397831\pi$
$480$		0			0
$481$	−806.850	−	1397.50i	−0.0764848	−	0.132476i
$482$	−9731.91	+	985.969i	−0.919661	+	0.0931736i
$483$		0			0
$484$	−10244.8	+	2097.40i	−0.962138	+	0.196976i
$485$		−	24538.7i		−	2.29741i
$486$		0			0
$487$		−	1992.29i		−	0.185378i	−0.995695	−	0.0926891i	$-0.970454\pi$
$487$		−	1992.29i		−	0.185378i	0.995695	−	0.0926891i	$-0.0295463\pi$
$488$	−7.94394	+	35.4091i	−0.000736896	+	0.00328462i
$489$		0			0
$490$	141.380	+	1395.48i	0.0130345	+	0.128656i
$491$	−4407.34	−	7633.75i	−0.405093	−	0.701642i	0.589239	−	0.807959i	$-0.299428\pi$
$491$	−4407.34	−	7633.75i	−0.405093	−	0.701642i	−0.994332	+	0.106317i	$0.966094\pi$
$492$		0			0
$493$	7825.94	−	13554.9i	0.714934	−	1.23830i
$494$	−2127.78	−	956.929i	−0.193792	−	0.0871544i
$495$		0			0
$496$	−20927.2	−	2517.54i	−1.89447	−	0.227905i
$497$	−6459.06	−	3729.14i	−0.582954	−	0.336569i
$498$		0			0
$499$	18252.9	−	10538.3i	1.63750	−	0.945409i	0.655806	−	0.754930i	$-0.272329\pi$
$499$	18252.9	−	10538.3i	1.63750	−	0.945409i	0.981691	−	0.190479i	$-0.0610042\pi$
$500$	3815.14	+	1271.34i	0.341236	+	0.113712i
$501$		0			0
$502$	4924.71	+	6832.04i	0.437850	+	0.607428i
$503$	19011.6			1.68526			0.842629	−	0.538494i	$-0.181006\pi$
$503$	19011.6			1.68526			0.842629	+	0.538494i	$0.181006\pi$
$504$		0			0
$505$	6073.31			0.535166
$506$	−1098.88	−	1524.47i	−0.0965434	−	0.133934i
$507$		0			0
$508$	−12734.9	−	4243.70i	−1.11224	−	0.370638i
$509$	−11096.0	+	6406.27i	−0.966250	+	0.557865i	−0.898091	−	0.439810i	$-0.855046\pi$
$509$	−11096.0	+	6406.27i	−0.966250	+	0.557865i	−0.0681588	+	0.997674i	$0.521712\pi$
$510$		0			0
$511$	−12986.7	−	7497.88i	−1.12426	−	0.649093i
$512$	−7122.13	+	9137.45i	−0.614759	+	0.788715i
$513$		0			0
$514$	16660.3	+	7492.64i	1.42968	+	0.642970i
$515$	−4503.53	+	7800.35i	−0.385339	+	0.667426i
$516$		0			0
$517$	−456.332	−	790.390i	−0.0388190	−	0.0672365i
$518$	−735.357	−	7258.27i	−0.0623740	−	0.615657i
$519$		0			0
$520$	−4462.09	−	1001.06i	−0.376299	−	0.0844218i
$521$			14455.7i			1.21558i	0.794100	+	0.607788i	$0.207943\pi$
$521$			14455.7i			1.21558i	−0.794100	+	0.607788i	$0.792057\pi$
$522$		0			0
$523$		−	15232.9i		−	1.27359i	−0.771032	−	0.636796i	$-0.780259\pi$
$523$		−	15232.9i		−	1.27359i	0.771032	−	0.636796i	$-0.219741\pi$
$524$	11167.1	−	2286.20i	0.930984	−	0.190598i
$525$		0			0
$526$	−16552.0	+	1676.93i	−1.37206	+	0.139007i
$527$	11733.4	+	20322.8i	0.969854	+	1.67984i
$528$		0			0
$529$	−3177.87	+	5504.23i	−0.261187	+	0.452390i
$530$	5172.84	−	11502.1i	0.423950	−	0.942675i
$531$		0			0
$532$	−6998.72	−	7891.13i	−0.570363	−	0.643090i
$533$	356.664	+	205.920i	0.0289847	+	0.0167343i
$534$		0			0
$535$	−6238.33	+	3601.70i	−0.504124	+	0.291056i
$536$	6574.05	−	7138.01i	0.529768	−	0.575215i
$537$		0			0
$538$	−6807.83	+	4907.27i	−0.545551	+	0.393248i
$539$	144.667			0.0115608
$540$		0			0
$541$	−23075.7			−1.83383			−0.916915	−	0.399083i	$-0.869328\pi$
$541$	−23075.7			−1.83383			−0.916915	+	0.399083i	$0.869328\pi$
$542$	4556.31	−	3284.31i	0.361089	−	0.260283i
$543$		0			0
$544$	12895.9	+	241.908i	1.01637	+	0.0190657i
$545$	13033.3	−	7524.80i	1.02438	−	0.591426i
$546$		0			0
$547$	317.151	+	183.107i	0.0247905	+	0.0143128i	0.512344	−	0.858780i	$-0.328777\pi$
$547$	317.151	+	183.107i	0.0247905	+	0.0143128i	−0.487554	+	0.873093i	$0.662111\pi$
$548$	160.540	−	142.385i	0.0125145	−	0.0110992i
$549$		0			0
$550$	878.056	−	1952.40i	0.0680735	−	0.151365i
$551$	7501.66	−	12993.2i	0.580002	−	1.00459i
$552$		0			0
$553$	−763.434	−	1322.31i	−0.0587061	−	0.101682i
$554$	−12221.2	+	1238.17i	−0.937236	+	0.0949542i
$555$		0			0
$556$	2657.92	+	12982.7i	0.202736	+	0.990272i
$557$			3402.66i			0.258842i	0.991590	+	0.129421i	$0.0413119\pi$
$557$			3402.66i			0.258842i	−0.991590	+	0.129421i	$0.958688\pi$
$558$		0			0
$559$			7.78437i			0.000588987i
$560$	−16541.6	−	12401.6i	−1.24823	−	0.935829i
$561$		0			0
$562$	−2222.80	−	21940.0i	−0.166839	−	1.64676i
$563$	−2461.45	−	4263.36i	−0.184259	−	0.319146i	0.759068	−	0.651012i	$-0.225655\pi$
$563$	−2461.45	−	4263.36i	−0.184259	−	0.319146i	−0.943327	+	0.331866i	$0.892322\pi$
$564$		0			0
$565$	3196.63	−	5536.73i	0.238023	−	0.412269i
$566$	−5276.53	−	2373.02i	−0.391854	−	0.176229i
$567$		0			0
$568$	8344.42	−	2607.82i	0.616416	−	0.192644i
$569$	−10423.8	−	6018.16i	−0.767990	−	0.443399i	0.0641669	−	0.997939i	$-0.479561\pi$
$569$	−10423.8	−	6018.16i	−0.767990	−	0.443399i	−0.832157	+	0.554540i	$0.812894\pi$
$570$		0			0
$571$	−522.706	+	301.784i	−0.0383092	+	0.0221178i	−0.519032	−	0.854755i	$-0.673708\pi$
$571$	−522.706	+	301.784i	−0.0383092	+	0.0221178i	0.480723	+	0.876872i	$0.340374\pi$
$572$	−149.113	+	447.472i	−0.0108999	+	0.0327093i
$573$		0			0
$574$	1088.74	+	1510.41i	0.0791694	+	0.109831i
$575$	−21100.5			−1.53035
$576$		0			0
$577$	−6971.52			−0.502995			−0.251497	−	0.967858i	$-0.580923\pi$
$577$	−6971.52			−0.502995			−0.251497	+	0.967858i	$0.580923\pi$
$578$	−271.180	−	376.207i	−0.0195149	−	0.0270729i
$579$		0			0
$580$	9297.10	−	27899.5i	0.665588	−	1.99735i
$581$	−15469.3	+	8931.22i	−1.10461	+	0.637745i
$582$		0			0
$583$	−1126.51	−	650.391i	−0.0800262	−	0.0462032i
$584$	16777.5	−	5243.34i	1.18880	−	0.371525i
$585$		0			0
$586$	6081.15	+	2734.88i	0.428686	+	0.192793i
$587$	−10334.9	+	17900.6i	−0.726691	+	1.25867i	0.231583	+	0.972815i	$0.425610\pi$
$587$	−10334.9	+	17900.6i	−0.726691	+	1.25867i	−0.958274	+	0.285851i	$0.907724\pi$
$588$		0			0
$589$	11247.2	+	19480.7i	0.786811	+	1.36280i
$590$	−995.659	−	9827.55i	−0.0694756	−	0.685752i
$591$		0			0
$592$	6842.15	+	5129.71i	0.475018	+	0.356132i
$593$		−	2417.22i		−	0.167392i	−0.996491	−	0.0836958i	$-0.973328\pi$
$593$		−	2417.22i		−	0.167392i	0.996491	−	0.0836958i	$-0.0266724\pi$
$594$		0			0
$595$			23017.2i			1.58590i
$596$	−1367.87	−	6681.40i	−0.0940100	−	0.459196i
$597$		0			0
$598$	4625.28	−	468.601i	0.316290	−	0.0320443i
$599$	−14467.5	−	25058.4i	−0.986852	−	1.70928i	−0.633400	−	0.773825i	$-0.718341\pi$
$599$	−14467.5	−	25058.4i	−0.986852	−	1.70928i	−0.353452	−	0.935453i	$-0.614992\pi$
$600$		0			0
$601$	−318.246	+	551.219i	−0.0215999	+	0.0374121i	−0.876623	−	0.481177i	$-0.840209\pi$
$601$	−318.246	+	551.219i	−0.0215999	+	0.0374121i	0.855023	+	0.518589i	$0.173543\pi$
$602$	−14.4346	+	32.0962i	−0.000977263	+	0.00217299i
$603$		0			0
$604$	−8791.25	+	7797.05i	−0.592237	+	0.525261i
$605$	18944.0	+	10937.3i	1.27303	+	0.734983i
$606$		0			0
$607$	−16616.3	+	9593.41i	−1.11109	+	0.641490i	−0.939112	−	0.343610i	$-0.888350\pi$
$607$	−16616.3	+	9593.41i	−1.11109	+	0.641490i	−0.171981	+	0.985100i	$0.555017\pi$
$608$	12361.5	+	231.885i	0.824548	+	0.0154674i
$609$		0			0
$610$	61.5791	−	44.3878i	0.00408732	−	0.00294625i
$611$	2257.80			0.149494
$612$		0			0
$613$	6429.22			0.423612			0.211806	−	0.977312i	$-0.432066\pi$
$613$	6429.22			0.423612			0.211806	+	0.977312i	$0.432066\pi$
$614$	−12668.4	+	9131.69i	−0.832660	+	0.600204i
$615$		0			0
$616$	−1444.57	+	1568.49i	−0.0944858	+	0.102591i
$617$	6024.79	−	3478.41i	0.393110	−	0.226962i	−0.290397	−	0.956906i	$-0.593787\pi$
$617$	6024.79	−	3478.41i	0.393110	−	0.226962i	0.683507	+	0.729944i	$0.260454\pi$
$618$		0			0
$619$	−19227.5	−	11101.0i	−1.24850	−	0.720819i	−0.277686	−	0.960672i	$-0.589567\pi$
$619$	−19227.5	−	11101.0i	−1.24850	−	0.720819i	−0.970809	+	0.239853i	$0.922901\pi$
$620$	29255.9	+	32986.4i	1.89508	+	2.13672i
$621$		0			0
$622$	1780.37	−	3958.75i	0.114769	−	0.255195i
$623$	−10079.0	+	17457.4i	−0.648168	+	1.12266i
$624$		0			0
$625$	5483.94	+	9498.47i	0.350972	+	0.607902i
$626$	−24669.3	+	2499.32i	−1.57505	+	0.159573i
$627$		0			0
$628$	21075.2	−	4314.68i	1.33916	−	0.274163i
$629$		−	9520.65i		−	0.603519i
$630$		0			0
$631$		−	529.250i		−	0.0333901i	−0.999861	−	0.0166950i	$-0.994686\pi$
$631$		−	529.250i		−	0.0333901i	0.999861	−	0.0166950i	$-0.00531444\pi$
$632$	1746.35	+	391.790i	0.109915	+	0.0246591i
$633$		0			0
$634$	1999.72	+	19738.0i	0.125266	+	1.23643i
$635$	14039.4	+	24317.0i	0.877383	+	1.51967i
$636$		0			0
$637$	−178.943	+	309.938i	−0.0111303	+	0.0192782i
$638$	−2766.27	−	1244.08i	−0.171658	−	0.0771997i
$639$		0			0
$640$	23828.5	−	4414.40i	1.47172	−	0.272648i
$641$	19866.3	+	11469.8i	1.22414	+	0.706755i	0.965797	−	0.259299i	$-0.0834915\pi$
$641$	19866.3	+	11469.8i	1.22414	+	0.706755i	0.258339	+	0.966054i	$0.416825\pi$
$642$		0			0
$643$	−2182.17	+	1259.88i	−0.133836	+	0.0772702i	−0.565423	−	0.824801i	$-0.691287\pi$
$643$	−2182.17	+	1259.88i	−0.133836	+	0.0772702i	0.431587	+	0.902071i	$0.357954\pi$
$644$	19939.7	+	6644.59i	1.22008	+	0.406574i
$645$		0			0
$646$	−8048.91	−	11166.2i	−0.490217	−	0.680076i
$647$	5938.61			0.360851			0.180426	−	0.983589i	$-0.442252\pi$
$647$	5938.61			0.360851			0.180426	+	0.983589i	$0.442252\pi$
$648$		0			0
$649$	−1018.81			−0.0616205
$650$	3096.77	+	4296.14i	0.186870	+	0.259244i
$651$		0			0
$652$	16594.8	+	5529.97i	0.996785	+	0.332163i
$653$	22562.1	−	13026.3i	1.35210	−	0.780638i	0.363561	−	0.931571i	$-0.381561\pi$
$653$	22562.1	−	13026.3i	1.35210	−	0.780638i	0.988544	+	0.150933i	$0.0482277\pi$
$654$		0			0
$655$	−20649.3	−	11921.9i	−1.23181	−	0.711184i
$656$	−2166.86	−	260.674i	−0.128966	−	0.0155146i
$657$		0			0
$658$	9309.24	+	4186.66i	0.551538	+	0.248044i
$659$	−14176.7	+	24554.8i	−0.838008	+	1.45147i	0.0535504	+	0.998565i	$0.482946\pi$
$659$	−14176.7	+	24554.8i	−0.838008	+	1.45147i	−0.891558	+	0.452907i	$0.850387\pi$
$660$		0			0
$661$	5168.04	+	8951.31i	0.304105	+	0.526725i	0.977062	−	0.212957i	$-0.0683093\pi$
$661$	5168.04	+	8951.31i	0.304105	+	0.526725i	−0.672957	+	0.739682i	$0.734976\pi$
$662$	−2819.02	−	27824.9i	−0.165505	−	1.63360i
$663$		0			0
$664$	4583.45	−	20430.2i	0.267880	−	1.19404i
$665$			22063.4i			1.28659i
$666$		0			0
$667$			29896.3i			1.73551i
$668$	−28068.1	+	5746.32i	−1.62573	+	0.332832i
$669$		0			0
$670$	−20195.6	+	2046.07i	−1.16451	+	0.117980i
$671$	−3.91468	−	6.78042i	−0.000225223	−	0.000390097i
$672$		0			0
$673$	7541.97	−	13063.1i	0.431979	−	0.748209i	−0.565065	−	0.825046i	$-0.691149\pi$
$673$	7541.97	−	13063.1i	0.431979	−	0.748209i	0.997044	+	0.0768374i	$0.0244822\pi$
$674$	−5810.05	+	12918.9i	−0.332040	+	0.738307i
$675$		0			0
$676$	10888.1	+	12276.4i	0.619486	+	0.698477i
$677$	11873.7	+	6855.26i	0.674065	+	0.389172i	0.797615	−	0.603167i	$-0.206095\pi$
$677$	11873.7	+	6855.26i	0.674065	+	0.389172i	−0.123550	+	0.992338i	$0.539428\pi$
$678$		0			0
$679$	24514.0	−	14153.2i	1.38551	−	0.799925i
$680$	−19845.8	−	18277.8i	−1.11919	−	1.03077i
$681$		0			0
$682$	3689.06	−	2659.17i	0.207128	−	0.149303i
$683$	−807.274			−0.0452262			−0.0226131	−	0.999744i	$-0.507199\pi$
$683$	−807.274			−0.0452262			−0.0226131	+	0.999744i	$0.507199\pi$
$684$		0			0
$685$	−448.867			−0.0250370
$686$	13879.5	−	10004.7i	0.772483	−	0.556826i
$687$		0			0
$688$	−16.2114	−	37.9332i	−0.000898333	−	0.00210202i
$689$	2786.82	−	1608.97i	0.154092	−	0.0889651i
$690$		0			0
$691$	19006.4	+	10973.4i	1.04636	+	0.604119i	0.921629	−	0.388072i	$-0.126859\pi$
$691$	19006.4	+	10973.4i	1.04636	+	0.604119i	0.124735	+	0.992190i	$0.460192\pi$
$692$	−653.130	+	579.268i	−0.0358790	+	0.0318215i
$693$		0			0
$694$	−9043.13	+	20107.9i	−0.494629	+	1.09983i
$695$	13860.3	−	24006.7i	0.756474	−	1.31025i
$696$		0			0
$697$	1214.91	+	2104.28i	0.0660228	+	0.114355i
$698$	25555.9	−	2589.14i	1.38582	−	0.140402i
$699$		0			0
$700$	4802.09	+	23456.0i	0.259289	+	1.26651i
$701$		−	3170.45i		−	0.170822i	−0.996346	−	0.0854110i	$-0.972780\pi$
$701$		−	3170.45i		−	0.170822i	0.996346	−	0.0854110i	$-0.0272203\pi$
$702$		0			0
$703$		−	9126.15i		−	0.489615i
$704$	−205.258	−	2491.06i	−0.0109886	−	0.133360i
$705$		0			0
$706$	−1298.55	−	12817.2i	−0.0692234	−	0.683263i
$707$	3502.90	+	6067.20i	0.186337	+	0.322745i
$708$		0			0
$709$	−1413.03	+	2447.45i	−0.0748485	+	0.129641i	−0.901020	−	0.433777i	$-0.857181\pi$
$709$	−1413.03	+	2447.45i	−0.0748485	+	0.129641i	0.826172	+	0.563418i	$0.190514\pi$
$710$	−16678.3	−	7500.76i	−0.881586	−	0.396477i
$711$		0			0
$712$	−7048.37	−	22553.2i	−0.370996	−	1.18710i
$713$	−38818.0	−	22411.6i	−2.03892	−	1.17717i
$714$		0			0
$715$	854.438	−	493.310i	0.0446912	−	0.0258025i
$716$	678.816	−	2037.05i	0.0354309	−	0.106324i
$717$		0			0
$718$	8956.10	+	12424.8i	0.465514	+	0.645805i
$719$	−15469.9			−0.802408			−0.401204	−	0.915989i	$-0.631408\pi$
$719$	−15469.9			−0.802408			−0.401204	+	0.915989i	$0.631408\pi$
$720$		0			0
$721$	−10390.0			−0.536677
$722$	3628.79	+	5034.20i	0.187049	+	0.259493i
$723$		0			0
$724$	−2272.65	+	6819.96i	−0.116661	+	0.350085i
$725$	−29494.0	+	17028.4i	−1.51087	+	0.872301i
$726$		0			0
$727$	−6900.11	−	3983.78i	−0.352009	−	0.203233i	0.313561	−	0.949568i	$-0.398478\pi$
$727$	−6900.11	−	3983.78i	−0.352009	−	0.203233i	−0.665570	+	0.746336i	$0.731811\pi$
$728$	−1573.55	−	5034.98i	−0.0801092	−	0.256331i
$729$		0			0
$730$	−33533.8	−	15081.2i	−1.70019	−	0.764629i
$731$	−22.9635	+	39.7739i	−0.00116188	+	0.00201244i
$732$		0			0
$733$	−12334.6	−	21364.2i	−0.621542	−	1.07654i	−0.989199	−	0.146581i	$-0.953173\pi$
$733$	−12334.6	−	21364.2i	−0.621542	−	1.07654i	0.367656	−	0.929962i	$-0.380160\pi$
$734$	3038.04	+	29986.7i	0.152774	+	1.50794i
$735$		0			0
$736$	−21563.0	+	11915.9i	−1.07992	+	0.596773i
$737$			2093.65i			0.104641i
$738$		0			0
$739$		−	1182.09i		−	0.0588414i	−0.999567	−	0.0294207i	$-0.990634\pi$
$739$		−	1182.09i		−	0.0588414i	0.999567	−	0.0294207i	$-0.00936624\pi$
$740$	−3587.76	−	17524.6i	−0.178228	−	0.870563i
$741$		0			0
$742$	14474.0	−	1466.41i	0.716116	−	0.0725519i
$743$	−13616.4	−	23584.4i	−0.672327	−	1.16450i	−0.977243	−	0.212125i	$-0.931962\pi$
$743$	−13616.4	−	23584.4i	−0.672327	−	1.16450i	0.304916	−	0.952379i	$-0.401372\pi$
$744$		0			0
$745$	−7133.00	+	12354.7i	−0.350782	+	0.607573i
$746$	3143.87	−	6990.55i	0.154296	−	0.343086i
$747$		0			0
$748$	−2081.90	+	1846.46i	−0.101767	+	0.0902584i
$749$	−7196.16	−	4154.70i	−0.351057	−	0.202683i
$750$		0			0
$751$	−12287.2	+	7093.99i	−0.597024	+	0.344692i	−0.767870	−	0.640606i	$-0.778683\pi$
$751$	−12287.2	+	7093.99i	−0.597024	+	0.344692i	0.170846	+	0.985298i	$0.445350\pi$
$752$	−11002.2	+	4701.99i	−0.533523	+	0.228010i
$753$		0			0
$754$	6087.01	−	4387.68i	0.294000	−	0.211923i
$755$	24580.1			1.18485
$756$		0			0
$757$	30482.1			1.46353			0.731764	−	0.681559i	$-0.238698\pi$
$757$	30482.1			1.46353			0.731764	+	0.681559i	$0.238698\pi$
$758$	14673.9	−	10577.4i	0.703141	−	0.506843i
$759$		0			0
$760$	−19023.4	−	17520.4i	−0.907965	−	0.836227i
$761$	19985.7	−	11538.8i	0.952013	−	0.549645i	0.0583074	−	0.998299i	$-0.481430\pi$
$761$	19985.7	−	11538.8i	0.952013	−	0.549645i	0.893706	+	0.448654i	$0.148096\pi$
$762$		0			0
$763$	15034.5	+	8680.15i	0.713348	+	0.411851i
$764$	2731.98	+	3080.33i	0.129371	+	0.145867i
$765$		0			0
$766$	1583.73	−	3521.51i	0.0747031	−	0.166106i
$767$	1260.19	−	2182.72i	0.0593258	−	0.102755i
$768$		0			0
$769$	−1035.31	−	1793.21i	−0.0485491	−	0.0840895i	0.840730	−	0.541455i	$-0.182126\pi$
$769$	−1035.31	−	1793.21i	−0.0485491	−	0.0840895i	−0.889279	+	0.457366i	$0.848793\pi$
$770$	4437.73	−	449.600i	0.207694	−	0.0210421i
$771$		0			0
$772$	−19274.8	+	3946.07i	−0.898594	+	0.183967i
$773$			35103.0i			1.63333i	0.577110	+	0.816666i	$0.304180\pi$
$773$			35103.0i			1.63333i	−0.577110	+	0.816666i	$0.695820\pi$
$774$		0			0
$775$		−	51061.1i		−	2.36667i
$776$	−7263.34	+	32375.4i	−0.336003	+	1.49769i
$777$		0			0
$778$	1771.38	+	17484.2i	0.0816285	+	0.805706i
$779$	1164.57	+	2017.09i	0.0535622	+	0.0927724i
$780$		0			0
$781$	−943.085	+	1633.47i	−0.0432090	+	0.0748402i
$782$	25015.0	+	11250.0i	1.14391	+	0.514450i
$783$		0			0
$784$	226.523	−	1882.98i	0.0103190	−	0.0857774i
$785$	−38970.7	−	22499.7i	−1.77188	−	1.02299i
$786$		0			0
$787$	−20621.0	+	11905.5i	−0.934000	+	0.539245i	−0.888074	−	0.459700i	$-0.847957\pi$
$787$	−20621.0	+	11905.5i	−0.934000	+	0.539245i	−0.0459253	+	0.998945i	$0.514624\pi$
$788$	4906.78	+	1635.11i	0.221823	+	0.0739192i
$789$		0			0
$790$	−2189.18	−	3037.04i	−0.0985918	−	0.136776i
$791$	7374.87			0.331505
$792$		0			0
$793$	19.3687			0.000867343
$794$	5444.17	+	7552.68i	0.243333	+	0.337575i
$795$		0			0
$796$	−13228.6	−	4408.24i	−0.589041	−	0.196289i
$797$	2079.48	−	1200.59i	0.0924202	−	0.0533588i	−0.453078	−	0.891471i	$-0.649674\pi$
$797$	2079.48	−	1200.59i	0.0924202	−	0.0533588i	0.545498	+	0.838112i	$0.316341\pi$
$798$		0			0
$799$	11536.1	+	6660.38i	0.510787	+	0.294903i
$800$	−24037.5	−	14485.9i	−1.06232	−	0.640190i
$801$		0			0
$802$	−10513.1	−	4728.06i	−0.462880	−	0.208171i
$803$	−1896.19	+	3284.29i	−0.0833312	+	0.144334i
$804$		0			0
$805$	−21982.3	−	38074.4i	−0.962451	−	1.66701i
$806$	1133.97	+	11192.7i	0.0495562	+	0.489140i
$807$		0			0
$808$	−8012.88	−	1797.67i	−0.348876	−	0.0782695i
$809$		−	29338.0i		−	1.27499i	−0.770453	−	0.637497i	$-0.779970\pi$
$809$		−	29338.0i		−	1.27499i	0.770453	−	0.637497i	$-0.220030\pi$
$810$		0			0
$811$		−	30884.9i		−	1.33726i	−0.743597	−	0.668629i	$-0.766882\pi$
$811$		−	30884.9i		−	1.33726i	0.743597	−	0.668629i	$-0.233118\pi$
$812$	33233.8	−	6803.86i	1.43630	−	0.294050i
$813$		0			0
$814$	−1835.59	+	185.969i	−0.0790386	+	0.00800764i
$815$	−18294.8	−	31687.5i	−0.786305	−	1.36192i
$816$		0			0
$817$	−22.0120	+	38.1258i	−0.000942596	+	0.00163262i
$818$	16368.6	−	36396.5i	0.699653	−	1.55571i
$819$		0			0
$820$	3029.25	+	3415.51i	0.129007	+	0.145457i
$821$	17356.7	+	10020.9i	0.737824	+	0.425983i	0.821277	−	0.570529i	$-0.193262\pi$
$821$	17356.7	+	10020.9i	0.737824	+	0.425983i	−0.0834539	+	0.996512i	$0.526595\pi$
$822$		0			0
$823$	5398.43	−	3116.78i	0.228648	−	0.132010i	−0.381300	−	0.924451i	$-0.624524\pi$
$823$	5398.43	−	3116.78i	0.228648	−	0.132010i	0.609948	+	0.792441i	$0.291190\pi$
$824$	8250.64	−	8958.43i	0.348816	−	0.378740i
$825$		0			0
$826$	9243.40	−	6662.89i	0.389369	−	0.280668i
$827$	43288.8			1.82019			0.910096	−	0.414397i	$-0.136007\pi$
$827$	43288.8			1.82019			0.910096	+	0.414397i	$0.136007\pi$
$828$		0			0
$829$	−15655.6			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$829$	−15655.6			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$830$	−35529.6	+	25610.7i	−1.48584	+	1.07104i
$831$		0			0
$832$	5590.79	+	2641.51i	0.232964	+	0.110070i
$833$	−1828.60	+	1055.74i	−0.0760592	+	0.0439128i
$834$		0			0
$835$	51901.4	+	29965.3i	2.15104	+	1.24191i
$836$	−1995.64	+	1769.95i	−0.0825605	+	0.0732237i
$837$		0			0
$838$	7388.04	−	16427.7i	0.304553	−	0.677189i
$839$	22793.5	−	39479.4i	0.937924	−	1.62453i	0.168588	−	0.985687i	$-0.446079\pi$
$839$	22793.5	−	39479.4i	0.937924	−	1.62453i	0.769336	−	0.638845i	$-0.220587\pi$
$840$		0			0
$841$	11932.2	+	20667.2i	0.489247	+	0.847400i
$842$	−30426.6	+	3082.61i	−1.24533	+	0.126168i
$843$		0			0
$844$	−6759.38	−	33016.5i	−0.275672	−	1.34653i
$845$		−	34324.6i		−	1.39740i
$846$		0			0
$847$			25233.2i			1.02364i
$848$	−10229.4	+	13644.2i	−0.414243	+	0.552529i
$849$		0			0
$850$	3149.44	+	31086.3i	0.127088	+	1.25441i
$851$	9092.58	+	15748.8i	0.366263	+	0.634386i
$852$		0			0
$853$	−1318.98	+	2284.55i	−0.0529439	+	0.0917016i	−0.891283	−	0.453448i	$-0.850194\pi$
$853$	−1318.98	+	2284.55i	−0.0529439	+	0.0917016i	0.838339	+	0.545150i	$0.183527\pi$
$854$	79.8601	+	35.9156i	0.00319995	+	0.00143912i
$855$		0			0
$856$	9296.68	−	2905.42i	0.371208	−	0.116011i
$857$	21068.1	+	12163.7i	0.839759	+	0.484835i	0.857182	−	0.515013i	$-0.172213\pi$
$857$	21068.1	+	12163.7i	0.839759	+	0.484835i	−0.0174233	+	0.999848i	$0.505546\pi$
$858$		0			0
$859$	38889.0	−	22452.6i	1.54468	−	0.891819i	0.546143	−	0.837692i	$-0.316096\pi$
$859$	38889.0	−	22452.6i	1.54468	−	0.891819i	0.998534	−	0.0541273i	$-0.0172377\pi$
$860$	−27.2803	+	81.8651i	−0.00108169	+	0.00324602i
$861$		0			0
$862$	−18140.8	−	25166.7i	−0.716797	−	0.994410i
$863$	3830.25			0.151081			0.0755406	−	0.997143i	$-0.475932\pi$
$863$	3830.25			0.151081			0.0755406	+	0.997143i	$0.475932\pi$
$864$		0			0
$865$	1826.14			0.0717809
$866$	−2466.15	−	3421.28i	−0.0967705	−	0.134249i
$867$		0			0
$868$	−16079.3	+	48252.0i	−0.628762	+	1.88684i
$869$	−334.406	+	193.070i	−0.0130540	+	0.00753675i
$870$		0			0
$871$	−4485.47	−	2589.69i	−0.174494	−	0.100744i
$872$	−19423.0	+	6070.11i	−0.754294	+	0.235734i
$873$		0			0
$874$	23978.5	+	10783.9i	0.928014	+	0.417357i
$875$	4851.74	−	8403.45i	0.187450	−	0.324673i
$876$		0			0
$877$	−12549.7	−	21736.6i	−0.483206	−	0.836938i	0.516608	−	0.856222i	$-0.327195\pi$
$877$	−12549.7	−	21736.6i	−0.483206	−	0.836938i	−0.999814	+	0.0192844i	$0.993861\pi$
$878$	634.574	+	6263.50i	0.0243916	+	0.240755i
$879$		0			0
$880$	−3136.32	+	4183.31i	−0.120143	+	0.160249i
$881$			3336.88i			0.127608i	0.997962	+	0.0638038i	$0.0203232\pi$
$881$			3336.88i			0.127608i	−0.997962	+	0.0638038i	$0.979677\pi$
$882$		0			0
$883$			26792.8i			1.02112i	0.859841	+	0.510561i	$0.170562\pi$
$883$			26792.8i			1.02112i	−0.859841	+	0.510561i	$0.829438\pi$
$884$	−1380.73	−	6744.25i	−0.0525329	−	0.256599i
$885$		0			0
$886$	44679.6	−	4526.62i	1.69418	−	0.171642i
$887$	13004.9	+	22525.1i	0.492290	+	0.852672i	0.999961	−	0.00887981i	$-0.00282657\pi$
$887$	13004.9	+	22525.1i	0.492290	+	0.852672i	−0.507670	+	0.861551i	$0.669493\pi$
$888$		0			0
$889$	−16195.0	+	28050.6i	−0.610983	+	1.05825i
$890$	−20272.9	+	45077.9i	−0.763539	+	1.69777i
$891$		0			0
$892$	−38415.4	+	34071.0i	−1.44198	+	1.27890i
$893$	11058.1	+	6384.40i	0.414384	+	0.239245i
$894$		0			0
$895$	−3889.71	+	2245.72i	−0.145272	+	0.0838729i
$896$	18153.5	+	21258.4i	0.676859	+	0.792627i
$897$		0			0
$898$	−26521.1	+	19117.1i	−0.985547	+	0.710408i
$899$	−72346.0			−2.68395
$900$		0			0
$901$	18985.5			0.701998
$902$	381.976	−	275.339i	0.0141002	−	0.0101638i
$903$		0			0
$904$	−5856.34	+	6358.74i	−0.215464	+	0.233948i
$905$	13022.6	−	7518.59i	0.478326	−	0.276162i
$906$		0			0
$907$	−23690.0	−	13677.4i	−0.867269	−	0.500718i	−0.000829418	−	1.00000i	$-0.500264\pi$
$907$	−23690.0	−	13677.4i	−0.867269	−	0.500718i	−0.866440	+	0.499282i	$0.833597\pi$
$908$	−11941.9	−	13464.6i	−0.436460	−	0.492113i
$909$		0			0
$910$	−4525.92	+	10063.6i	−0.164871	+	0.366599i
$911$	2661.94	−	4610.61i	0.0968100	−	0.167680i	−0.813553	−	0.581491i	$-0.802469\pi$
$911$	2661.94	−	4610.61i	0.0968100	−	0.167680i	0.910363	+	0.413812i	$0.135803\pi$
$912$		0			0
$913$	2258.67	+	3912.14i	0.0818742	+	0.141810i
$914$	30643.8	−	3104.62i	1.10898	−	0.112354i
$915$		0			0
$916$	27201.6	−	5568.92i	0.981187	−	0.200876i
$917$		−	27504.7i		−	0.990495i
$918$		0			0
$919$			3951.52i			0.141837i	0.997482	+	0.0709187i	$0.0225931\pi$
$919$			3951.52i			0.141837i	−0.997482	+	0.0709187i	$0.977407\pi$
$920$	50284.4	+	11281.2i	1.80199	+	0.404271i
$921$		0			0
$922$	−3357.04	−	33135.3i	−0.119911	−	1.18357i
$923$	−2333.06	−	4040.97i	−0.0831999	−	0.144106i
$924$		0			0
$925$	−10358.0	+	17940.5i	−0.368181	+	0.637708i
$926$	−6861.49	−	3085.82i	−0.243502	−	0.109510i
$927$		0			0
$928$	−20524.3	+	34057.6i	−0.726017	+	1.20474i
$929$	−2705.24	−	1561.87i	−0.0955394	−	0.0551597i	0.451469	−	0.892287i	$-0.350900\pi$
$929$	−2705.24	−	1561.87i	−0.0955394	−	0.0551597i	−0.547008	+	0.837127i	$0.684233\pi$
$930$		0			0
$931$	−1752.83	+	1012.00i	−0.0617044	+	0.0356250i
$932$	−29240.6	−	9743.98i	−1.02769	−	0.342462i
$933$		0			0
$934$	54.5378	+	75.6601i	0.00191063	+	0.00265061i
$935$	5820.96			0.203600
$936$		0			0
$937$	24002.2			0.836838			0.418419	−	0.908254i	$-0.362584\pi$
$937$	24002.2			0.836838			0.418419	+	0.908254i	$0.362584\pi$
$938$	−13692.2	−	18995.1i	−0.476616	−	0.661208i
$939$		0			0
$940$	23744.3	+	7912.44i	0.823888	+	0.274548i
$941$	−42104.3	+	24308.9i	−1.45862	+	0.842135i	−0.998944	−	0.0459518i	$-0.985368\pi$
$941$	−42104.3	+	24308.9i	−1.45862	+	0.842135i	−0.459676	+	0.888086i	$0.652035\pi$
$942$		0			0
$943$	−4019.34	−	2320.57i	−0.138799	−	0.0801358i
$944$	−1595.27	+	13260.8i	−0.0550019	+	0.457205i
$945$		0			0
$946$	8.11700	+	3.65047i	0.000278971	+	0.000125462i
$947$	−9870.34	+	17095.9i	−0.338694	+	0.586635i	−0.984187	−	0.177131i	$-0.943318\pi$
$947$	−9870.34	+	17095.9i	−0.338694	+	0.586635i	0.645493	+	0.763766i	$0.276652\pi$
$948$		0			0
$949$	−4690.89	−	8124.86i	−0.160456	−	0.277918i
$950$	3018.94	+	29798.2i	0.103103	+	1.01766i
$951$		0			0
$952$	6812.96	−	30367.9i	0.231943	−	1.03385i
$953$			47895.5i			1.62800i	0.580863	+	0.814002i	$0.302715\pi$
$953$			47895.5i			1.62800i	−0.580863	+	0.814002i	$0.697285\pi$
$954$		0			0
$955$		−	8612.54i		−	0.291827i
$956$	−312.454	+	63.9678i	−0.0105706	+	0.00216409i
$957$		0			0
$958$	22900.9	−	2320.16i	0.772334	−	0.0782474i
$959$	−258.893	−	448.416i	−0.00871751	−	0.0150992i
$960$		0			0
$961$	39338.4	−	68136.1i	1.32048	−	2.28714i
$962$	1872.07	−	4162.64i	0.0627421	−	0.139510i
$963$		0			0
$964$	−18358.0	−	20698.8i	−0.613352	−	0.691561i
$965$	35641.4	+	20577.6i	1.18895	+	0.686441i
$966$		0			0
$967$	−39942.4	+	23060.8i	−1.32830	+	0.766892i	−0.985036	−	0.172349i	$-0.944864\pi$
$967$	−39942.4	+	23060.8i	−1.32830	+	0.766892i	−0.343259	+	0.939241i	$0.611531\pi$
$968$	−21756.5	−	20037.5i	−0.722397	−	0.665321i
$969$		0			0
$970$	56303.3	−	40584.9i	1.86370	−	1.34340i
$971$	−51058.5			−1.68748			−0.843741	−	0.536751i	$-0.819651\pi$
$971$	−51058.5			−1.68748			−0.843741	+	0.536751i	$0.819651\pi$
$972$		0			0
$973$	31976.7			1.05357
$974$	4571.24	−	3295.07i	0.150382	−	0.108399i
$975$		0			0
$976$	−94.3835	+	40.3364i	−0.00309543	+	0.00132289i
$977$	−19394.5	+	11197.4i	−0.635093	+	0.366671i	−0.782722	−	0.622372i	$-0.786169\pi$
$977$	−19394.5	+	11197.4i	−0.635093	+	0.366671i	0.147629	+	0.989043i	$0.452836\pi$
$978$		0			0
$979$	4414.92	+	2548.95i	0.144128	+	0.0832124i
$980$	−2968.05	+	2632.39i	−0.0967457	+	0.0858047i
$981$		0			0
$982$	10226.0	−	22738.0i	0.332307	−	0.738900i
$983$	−6698.78	+	11602.6i	−0.217353	+	0.376466i	−0.953998	−	0.299813i	$-0.903076\pi$
$983$	−6698.78	+	11602.6i	−0.217353	+	0.376466i	0.736645	+	0.676280i	$0.236409\pi$
$984$		0			0
$985$	−5409.43	−	9369.40i	−0.174983	−	0.303080i
$986$	44044.7	−	4462.30i	1.42259	−	0.144126i
$987$		0			0
$988$	−1323.52	−	6464.80i	−0.0426182	−	0.208171i
$989$		−	87.7240i		−	0.00282049i
$990$		0			0
$991$			24672.3i			0.790858i	0.918496	+	0.395429i	$0.129404\pi$
$991$			24672.3i			0.790858i	−0.918496	+	0.395429i	$0.870596\pi$
$992$	−28835.3	−	52180.5i	−0.922904	−	1.67009i
$993$		0			0
$994$	−2126.33	−	20987.8i	−0.0678503	−	0.669709i
$995$	14583.8	+	25259.8i	0.464660	+	0.804815i
$996$		0			0
$997$	−29032.1	+	50285.1i	−0.922223	+	1.59734i	−0.126255	+	0.991998i	$0.540296\pi$
$997$	−29032.1	+	50285.1i	−0.922223	+	1.59734i	−0.795968	+	0.605339i	$0.793038\pi$
$998$	54368.4	+	24451.2i	1.72445	+	0.775539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.h.b.35.9		24
3.2	odd	2		36.4.h.b.11.4	yes	24
4.3	odd	2	inner	108.4.h.b.35.12		24
9.2	odd	6		324.4.b.c.323.10		24
9.4	even	3		36.4.h.b.23.1	yes	24
9.5	odd	6	inner	108.4.h.b.71.12		24
9.7	even	3		324.4.b.c.323.15		24
12.11	even	2		36.4.h.b.11.1	✓	24
36.7	odd	6		324.4.b.c.323.9		24
36.11	even	6		324.4.b.c.323.16		24
36.23	even	6	inner	108.4.h.b.71.9		24
36.31	odd	6		36.4.h.b.23.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.1	✓	24	12.11	even	2
36.4.h.b.11.4	yes	24	3.2	odd	2
36.4.h.b.23.1	yes	24	9.4	even	3
36.4.h.b.23.4	yes	24	36.31	odd	6
108.4.h.b.35.9		24	1.1	even	1	trivial
108.4.h.b.35.12		24	4.3	odd	2	inner
108.4.h.b.71.9		24	36.23	even	6	inner
108.4.h.b.71.12		24	9.5	odd	6	inner
324.4.b.c.323.9		24	36.7	odd	6
324.4.b.c.323.10		24	9.2	odd	6
324.4.b.c.323.15		24	9.7	even	3
324.4.b.c.323.16		24	36.11	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +O(q^{10})\)	\(q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +(43.1673 + 19.4137i) q^{10} +(2.44092 - 4.22780i) q^{11} +(6.03848 + 10.4590i) q^{13} +(5.50343 + 54.3211i) q^{14} +(-51.2068 - 38.3909i) q^{16} +71.2528i q^{17} +68.3003i q^{19} +(26.8509 + 131.154i) q^{20} +(13.7376 - 1.39180i) q^{22} +(-68.0491 - 117.865i) q^{23} +(77.5192 - 134.267i) q^{25} +(-14.0106 + 31.1533i) q^{26} +(-115.536 + 102.470i) q^{28} +(-190.237 - 109.833i) q^{29} +(285.221 - 164.672i) q^{31} +(3.39507 - 180.987i) q^{32} +(-163.487 + 117.846i) q^{34} +323.035 q^{35} -133.618 q^{37} +(-156.713 + 112.963i) q^{38} +(-256.520 + 278.526i) q^{40} +(29.5326 - 17.0507i) q^{41} +(0.558209 + 0.322282i) q^{43} +(25.9142 + 29.2186i) q^{44} +(157.889 - 351.074i) q^{46} +(93.4753 - 161.904i) q^{47} +(14.8169 + 25.6636i) q^{49} +(436.282 - 44.2010i) q^{50} +(-94.6525 + 19.3780i) q^{52} -266.453i q^{53} -81.6944i q^{55} +(-426.199 - 95.6168i) q^{56} +(-62.6263 - 618.147i) q^{58} +(-104.347 - 180.734i) q^{59} +(0.801886 - 1.38891i) q^{61} +(849.565 + 382.076i) q^{62} +(420.885 - 291.548i) q^{64} +(175.024 + 101.050i) q^{65} +(-371.407 + 214.432i) q^{67} +(-540.787 - 180.209i) q^{68} +(534.272 + 741.193i) q^{70} -386.365 q^{71} -776.832 q^{73} +(-220.992 - 306.582i) q^{74} +(-518.378 - 172.742i) q^{76} +(81.6122 - 47.1188i) q^{77} +(-68.5000 - 39.5485i) q^{79} +(-1063.33 - 127.919i) q^{80} +(87.9665 + 39.5613i) q^{82} +(-462.668 + 801.365i) q^{83} +(596.185 + 1032.62i) q^{85} +(0.183763 + 1.81382i) q^{86} +(-24.1811 + 107.784i) q^{88} +1044.26i q^{89} +233.130i q^{91} +(1066.66 - 218.375i) q^{92} +(526.083 - 53.2991i) q^{94} +(571.481 + 989.834i) q^{95} +(733.184 - 1269.91i) q^{97} +(-34.3784 + 76.4422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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